Just on the basis of my own experience, it does indeed seem to be the case that a disproportionate number of undergraduate philosophy majors in coed institutions of higher education are male. (The same disproportion is to be found in the profession itself.) I'm not sure whether the data has been collected, although you might just do a simple Google search to see if anything comes up. I can only speculate why such a disproportion exists. It may in part have to do with the fact, noted above, that the overwhelming majority of faculty members in philosophy departments are male; it may have something to do with the nature of philosophy itself, which, on account of its focus on arguments, can often be seen as combative--although, of course, it need not be, and at its best, probably should not be--and such intellectual combat seems to be coded male. Philosophy courses may be seen as part of an 'argument culture' that puts off certain female students while attracting male students, therefore accounting for the disproportionate number of male as opposed to female undergraduate philosophy majors. For a perceptive exploration of the nature of and problems associated with the argument culture, you might check out Deborah Tannen, The Argument Culture: Stopping America's War on Words: Chapter 6, "Boys Will be Boys: Gender and Opposition," treats the issue of the relation between gender and the 'argument culture'.
Russell's History of Western Philosophy, while consistently entertaining, and worth reading on that score, is not a reliable source for knowledge about the philosophers it treats. The work may be not altogether unfairly described as one of the several 'shilling shockers' that Russell, who always needed money, wrote: sales of the History of Western Philosophy guaranteed Russell's financial security for the rest of his life.
I myself don't know of a good single-volume history of Western philosophy. Anthony Kenny has written multiple volumes on the history of Western philosophy; there is also a very fine series, published by Oxford University Press, with volumes covering various periods in the history of Western philosophy, including Terence Irwin on Classical Thought, John Cottingham on the Rationalists, and Roger Woolhouse on the Empiricists, but I can't vouch for the quality of the other volumes. Perhaps other respondents know of a good single-volume treatment of the history of Western philosophy; although I may be mistaken, I am incline to think that such works have fallen victim to the rise of specialization.
There aren't a whole lot of textbooks on this sort of thing. A more current text is John Burgess's Philosophical Logic. And, depending upon your interests, you might have a look at something like Graham Priest's Introduction to Non-classical Logic. Working through a serious textbook on modal logic would also be worth doing. The two classics are by Chellas and by Hughes and Cresswell.
A quite different route would be to look into linguistic semantics. Many forms of philosophical logic—tense logic, modal logic, epistemic logic—originated as attempts to deal with some of the features of natural language that are omitted by quantification theory. But the relation between the logical treatments and natural language were always pretty obscure, and around 1960 people started to get much more serious about dealing with natural language in its own terms. Formally, much of linguistic semantics looks like philosophical logic (especially in certain traditions), but it is targeted at an empirical phenomenon (natural language) and so its adequacy is subject to empirical constraints. That makes it very different, in the end. Two good places to start with this are Larson and Segal's text Knowledge of Meaning and Chierchia and McConnell-Ginet's Meaning and Grammar. The latter is on Google books, so you can have a peek before buying.
1. I don't think there is any reason to suppose that learning about mathematical logic from Principia to Gödel will be any help at all in understanding what is going on with the Frankfurt School. (The only tenuous connection I can think of is that the logical positivists were influenced by developments in logic, and the Frankfurt School were concerned inter alia to give a critique of positivism. But since neither the authors of Principia nor Gödel were positivists, it would be better to read some of the positivists themselves if you want to know what the Frankfurt School were reacting against).
2. Of course, I think finding out a bit about mathematical logic is fun for its own sake: but it is mathematics and to really understand I'm afraid there is not much for it other than working through some increasingly tough books called the likes of "An Introduction to Logic" followed by "Intermediate Logic" and then "Mathematical Logic". Still, you can get a distant impression of what's going on by following links on Wikipedia etc. And on Gödelian matters, Hofstadter's long book is entertainingly illuminating and somewhat annoying in about equal measure. Goldstein's book, though, is hopeless as a guide: see http://math.stanford.edu/~feferman/papers/lrb.pdf for an authoritative demolition (which indeed pulls its punches). If I was going to recommend one book on Gödel as a way in for the non-mathematical, it would be Torkel Franzen's Gödel's Theorem, an Incomplete Guide to its Use and Abuse.
Yes, there are seminal works of philosophy that are of historical and systematic interest for the understanding they convey of what philosophy is. Here I would mention at least a dozen historical works before any more recent academic papers - works by the usual suspects: Plato, Aristotle, Descartes, Hobbes, Locke, Hume Rousseau, Kant, Hegel, Marx, Mill, Frege, and Wittgenstein. With regard to academic papers - by which I take you to mean shorter works published in the last 60 years or so - there is no settled canon. Still, it is pretty clear who have been the leading philosophers of this period; and pretty clear also, in most cases, what their most important essays were. It would be difficult to understand the current state of Anglophone philosophy without having read at least a good smattering of the following: W.V.O. Quine's "Two Dogmas of Empiricism" and "Epistemology Naturalized", Donald Davidson's "On the Very Idea of a Conceptual Scheme", Philippa Foot's "The Problem of Abortion and the Doctrine of Double Effect", Robert Nozick's "Coercion", Derek Parfit's "Personal Identity" and "Equality or Priority", Tom Nagel's "What is it Like to be a Bat?", Bernard Williams' "Moral Luck", Ronald Dworkin's "Taking Rights Seriously", Peter Singer's "Famine, Affluence, and Morality" and a few other seminal works by Elizabeth Anscombe, Ruth Marcus, Saul Kripke, Hilary Putnam, David Lewis, Thomas Kuhns, John Rawls, John McDowell, Jerry Fodor, Patricia Churchland, Dan Dennett, and part-timers Noam Chomsky and Amartya Sen.
There are 2 ways to interpret your question. One way is as a request for information about the philosophy of engineering. If that's what you're asking, I can suggest two good books to start with:
Florman, Samuel C. (1994), The Existential Pleasures of Engineering, 2nd edition (New York: St. Martin's Press).
Davis, Michael (1998), Thinking Like an Engineer: Studies in the Ethics of a Profession (New York: Oxford University Press).
The first was written by a practicing engineer, the second by a philosopher. Both deal with questions like: What is engineering? How should engineers behave? You might find some other references on the webpage "What Is Engineering?" for my Philosophy of Computer Science course.
There is also a branch of philosophy called the philosophy of technology, which deals with related issues. Check the article with that title in the Stanford Encyclopedia of Philosophy.
The other interpretation is as a request for information about how to apply philosophical thinking to engineering. Here, I would think that the best answer is that the kind of analytical thinking skills that are the mark of good philosophy would stand you in good stead when dealing with engineering problems.
Another relatively recent, good, general introduction to a variety of philosophical issues is Thomas Nagel, What Does it All Mean?, which I myself read in my first year of graduate school and found most illuminating. Bertrand Russell's The Problems of Philosophy is a classic from relatively early in the twentieth century.
You might also consider reading some of the canonical texts of Western philosophy (in my ignorance, I don't know Eastern philosophy, and so am not in a position to recommend any works of Eastern philosophy): a good place to begin is with Plato's 'Socratic' dialogues, the Apology, Euthyphro, and Crito; if you like those dialogues, you might move on to the Republic, which treats many of the problem areas of philosophy, including epistemology (the nature of knowledge), metaphysics (the nature of what there is), ethics, and aesthetics, among other areas; a couple of more 'modern' works that you might consider are Descartes's Meditations on First Philosophy (which focuses on issues in epistemology and metaphysics), and Kant's Groundwork of the Metaphysics of Morals, which tries to lay a foundation (hence the word in the title translated as 'Groundwork' by certain translators) for morality and hence treats ethics; if you want to grapple with some twentieth-century philosophy from the 'Continental' tradition, you might start with something like Jean-Paul Sartre's Existentialism and Human Emotions. This is just a short selection, of course--other panelists would of course suggest other works!!
In Between Man and Man, Martin Buber recounts the following story, which he takes to illuminate the experience at the heart of I and Thou:
"When I was eleven years of age, spending the summer on my grandparents' estate, I used, as often as I could do it unobserved, to steal into the stable and gently stroke the neck of my darling, a broad dapplegray horse. It was not a casual delight but a great, certainly friendly, but also deeply stirring happening. If I am to explain it now, beginning from the still very fresh memory of my hand, I must say that what I experienced in touch with the animal was the Other, the immense otherness of the Other, which, however, did not remain strange like the otherness of the ox and the ram, but rather let me draw near and touch it. When I stroked the mighty mane, sometimes marvelously smooth-combed, at other times just as astonishingly wild, and felt the life beneath my hand, it was as though the element of vitality itself bordered on my skin, something that was not I, was certainly not akin to me, palpably the other, not just another, really the Other itself; and yet it let me approach, confided itself to me, placed itself elementally in the relation of Thou and Thou with me. The horse, even when I had not begun by pouring oats for him into the manger, very gently raised his massive head, ears flicking, then snorted quietly, as a conspirator gives a signal meant to be recognizable only by his fellow-conspirator; and I was approved. But once--I do not know what came over the child, at any rate it was childlike enough--it struck me about the stroking, what fun it gave me, and suddenly I became conscious of my hand. The game went on as before, but something changed, it was no longer the same thing. And the next day, after giving him a rich feed, when I stroked my friend's head he did not raise his head. A few years later, when I thought back to the incident, I no longer supposed that the animal had noticed my defection. But at the time I considered myself judged" (p. 11).
Since Buber's work, in accordance with the phenomenological tradition to which he may be taken to belong, seeks to illuminate fundamental structures of human experience, one way to begin to grasp the concepts explicated in I and Thou is to try to recreate the sort of experience that Buber claims led him to recognize the relation between I and Thou at the heart of that work. (This is not meant to be a flip response to the question, but rather to suggest a way to begin to engage, experientially, with his claims, in just the way that phenomenology, generally, is meant to bring people back to the things themselves, the fundamental structures of human experience that are obscured to us because we take them for granted.)
But experience alone will probably not suffice to illuminate I and Thou. There are numerous books on Buber's thought. The following books were recommended to me by Professor Michael Morgan of Indiana University, an expert on Jewish Philosophy (certain of the books seem to me to be more 'academic' than others; the first one listed seems to me to be the most accessible, and the others are listed in what I take to be ascending order of difficulty--although I haven't been able to read through all the books myself, only to scan certain pages on the Web: Malcolm Diamond, Martin Buber: Jewish Existentialist; Laurence Silberstein, "Martin Buber's Social and Religious Thought: Alienation and the Quest for Meaning; Paul Mendes-Flohr, From Mysticism to Dialogue: Martin Buber's Transformation of German Social Thought.
I hope that these suggestions prove useful: I wish you good luck grappling with Buber's difficult, fascinating text!
Peter Smith's advice is dead on. The only thing I would add is that, while you are looking through the Stanford Encyclopedia and Phil Index and PhilPapers (which is a great resource), you look for recent articles whose titles or abstracts suggest that they provide an overview of the debate (e.g., "Recent Work on X"), and then you use the references in those articles to guide you towards other sources. Reading such articles often provides information about which sources will be most useful to you, given your interest in the debate. And don't forget to read the classic works (e.g., most cited) in the history of the debate as well.
Finally, you will make your future self much happier if you keep your sources well-organized (in electronic or real-world files) and if you jot down a few sentences about each article--its main point and how it might be relevant (or not) to your project. My current self is unhappy with my past selves for not being diligent enough about such record-keeping!