Do philosophers avoid figures of speech in peer reviewed philosphy journals?
By "figures of speech", I'll assume you mean something like metaphor. And, if so, then, no, philosophers do not avoid metaphor, at least not entirely. Here is one of my favorite philosophical metaphors, from W. V. O. Quine: "The lore of our fathers is a fabric of sentences. ...It is a pale gray lore, black with fact and white with convention. But I have found no substantial reasons for concluding that there are any quite black threads in it, or any white ones." Quine would later describe that lore as a "web", which has proven very fruitful.
What is true is that philosophers (at least the philosophers I know) try not to settle for such metaphors. One tries to "unpack" the metaphor, and make the underlying point as explicit as possible. But it is, I think, pretty widely appreciated that there is a limit to how far one can go in that direction. Really good metaphors are, as people who work on metaphor say, "inexhaustible", in some sense. There's always more you can dig out of them. That's maybe not true of the metaphor from Quine just quoted, but there are tons of quite striking examples in Donald Davidson's paper "What Metaphors Mean". (There's also a lot of irony there, since Davidson's view is precisely that metaphors have no meaning beyond their literal meaning.)
Why don't analytic philosphers in the Anglosphere take a stronger stand against
The question seems to presume that it is the job of philosophers as such to take such stands, and that seems wrong to me. Whether psychoanalysis is a helpful form of treatment, and for what conditions, just isn't the kind of question philosophers are well-placed to answer. In particular, whether psychoanalysis is or is not consistent with "medical findings" is presumably something one would have to answer by looking into the relevant medical and psychological literature. That's not what a job that philosophers, for the most part, are trained to do.
I have a very basic question that greatly puzzles me. Why do we consider
I guess I too am a bit confused. Surely philosophers have been questioning Plato's notion of forms ever since Plato. And one could presumably say the same thing about any other example one might care to offer. One could even object to the idea that a chair is any object designed for sitting. Surely there are chairs no one designed for that purpose, but are merely used for that purpose. But is anything that is used for sitting a chair? No, since sofas are also used for sitting, as are benches, tables, and old stumps. So what exactly is a chair? That's the kind of question that gets philosophy started.
This particular question isn't so interesting in itself, of course. The question philosophers really debate concerns the terms in which such questions are to be answered. And if such questions seem unimportant or useless, then consider the question what species are and how they are to be individuated. This is a question discussed by both biologists themselves and by philosophers of biology, and many of the issues there are familiar from more general philosophical discussion about the nature of kinds. Another area where this kind of issue becomes important is in the philosophy of race (and, similarly, of gender), where the nature of racial classification is a fundamental issue. What exactly is it to be black, or white, or Asian, or whatever?
Since programming languages are supposed to be ways to express logical processes
I'm not sure about the relationship to Plato's theory of ideas, but there are many connections between programming and philosophy. I'll mention just a few.
Some of the earliest investigations into natural language semantics appealed to ideas connected to the notion of compilation. Roughly, the thought was that understanding an uttered sentence might be something like compiling a program, i.e., translating it into the "machine language" of the brain. My own view, which is probably the majority view, is that this is seriously confused, but it has been attractive to many people.
The idea that "the mind is the software of the brain" has also been very attractive, since it was first articulated (though not quite in those terms) by the great British logician Alan Turing. There are many ways to implement this idea, perhaps the most familiar of them being the various forms of functionalism.
Finally, philosophers are often interested in formal languages, and software languages are certainly a variety of such languages. They are different from the usual languages we consider, because they tend to contain not assertions but rather instructions, so they are more "imperative" than "declarative". But I think they would nonetheless repay attention from philosophers of language.
Are philosophical thought experiments just cases of reasoning about counter
We rarely, if ever, see headlines such as "A team oh philosophers in Berlin
I don't know what the reasons are, but I think co-authored papers and books are becoming more common, especially in the more technical parts of philosophy (language, epistemology, etc). I could be wrong about that, as I haven't done an extensive study, but that's my sense.
Part of the reason may just have to do with technology. Working on some philosophical problem is a very ill-defined process much of the time. Just writing a paper can be a very long process. When things had to be snail-mailed back and forth, it was difficult to work with anyone not down the hall. Now, of course, collaboration is much easier, both in the developmental phases and in the writing phases, and so, as I said, we are seeing more of it. People can have a quick conversation at a conference, hit on an idea, and then develop it over email, the phone (which is much cheaper than it used to be), Skype, or whatever, and then write the paper without ever having to be physically in the same place again.
I presently working through Grayling's Introduction to Philosophical Logic
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.
Are there false or illegitimate philosophies, and if so, who's to say which ones
Yes, and me.
I'm not sure what the worry is here. I think it's clear that there are some philosophical views that are plainly wrong. There may be some truth in them somewhere, but research over the years has shown that the view is wrong. (Examples: Plato's theory of forms; Hobbes's theory of government.) So who says they're wrong? Well, the people who have done the research mentioned. This is no different from science. There are scientific theories that are wrong, and the people who say so are the scientists who do the work.
How do philosophers (or academics in general) justify their choice of profession
How does anyone (not just philosophers or other academics) justify a choice of profession? One does what one is good at and what one likes to do.
Academics in particular (philosophers included) need not apologize for their choice; we are, after all, teachers (in addition to being [perhaps] ivory-towerish scholars or researchers), and teachers surely serve the greater good. We philosophers, in particular, encourage critical (and skeptical) thinking, which--I suggest--is a Good Thing even if what we critique might be whether or not material objects are mereological sums of simples (or something equally esoteric).
Some of us do try to help solve practical problems (and Karl Marx once observed that philosophers have only tried to understand the world but that the point is to change it--I would imagine those are fighting words to some, inspiring to others!). Yes, my analysis of Wittgenstein or, more obscurely, Meinong might not directly improve people's lives, but then again how would we prove that? Maybe my analysis of Meinong in a course might inspire some student to further study of philosophy and that might lead in turn to her studying artificial intelligence (yes, there is a link!--see some of my own publications :-), which might lead to some breakthrough in applications of AI to medicine.