A further consideration is that, given that many people have strong wishes -- whether rationally grounded or not -- that their corpses and probably those of their loved ones be treated in certain ways, it would be highly upsetting to many if they were to become aware that such treatment quite possibly wouldn't be provided. In other words, even if you can't harm someone after they are dead, you can harm the living by treating the dead in ways of which the living disapprove.
The obvious place to start is with Descartes' *Meditations*. If you're short of time, you could read just the first two. Alongside you might find helpful ch. 4 of *Philosophy: The Basics* by Nigel Warburton. If you're then feeling a bit braver, you might try Tony Brueckner's article 'Brains in a Vat' in the excellent Stanford Encyclopedia of Philosophy -- there's a link to this from this website, on the right-hand side. Brueckner has more suggestions on reading. Good luck!
You seem to be raising a couple of puzzles here. One is how it has come about that human beings are sometimes motivated to help strangers, given that we might have expected evolution to produce beings concerned to promote the survival only of themselves and their kin. One immediate answer to this question is that, despite what some fanatical sociobiologists say, you can't explain everything about human behaviour as it is now merely by reference to our evolutionary history -- even if you allow in cultural as well as biological evolution. Evolution made it possible for impartial benevolence to develop, but it didn't necessitate it. Its emergence -- where it has emerged -- is to be understood primarily in terms of history rather than biology.
The second puzzle is why we *should* help others even when doing so doesn't benefit us. Many people have believed egoism -- the view that the only reason we have to do anything is grounded in the promotion of our own well-being. Philosophy has so far failed to provide a knock-down argument against egoism. But what it has clarified is some of its implications -- for example, that the fact that I can save you from years of agony by pushing some button gives me no reason to push that button.
There's an important difference between airing one's beliefs or preferences and merely possessing them. Many feel that criticizing people for beliefs is unfair, since beliefs aren't voluntary and one can be held responsible only for what's voluntary. But some philosophers doubt this (see e.g. Robert M. Adams's wonderful paper 'Involuntary Sins'). Imagine someone whose beliefs about homosexuality are unusually vicious -- perhaps they think gays should be tortured. Even if we think this person's beliefs are involuntary, we'll probably be tempted to criticize them. (It may be, of course, that this kind of criticism is of a different kind from that we use in the case of voluntary action.)
But this general didn't just hold these beliefs. He uttered them, and that is something that he could be held responsible for in the ordinary sense. Here I suspect people might want to criticize him from two angles. First, it might be thought that he was violating some principle of professional ethics. He was speaking as a member of the US army, and shouldn't have said anything that was against US army policy or might plausibly be seen as bringing the army into disrepute. Second, his comment raises questions about the limits of freedom of speech, most famously discussed in J.S. Mill's *On Liberty*. What one thinks about such limits is going to depend on one's general moral view. But something like Mill's view is quite common: that speech can be criticized if it is potentially harmful to others. Given that people often attack or discriminate against gays, speech that encourages such action should be criticized.
I suspect part of what you may be getting at is a contrast between explicit or articulated argument or deduction on the one hand (which you call 'logic') and a kind of 'seeing' on the other (which you call intuition). Either seem to be a respectable way of arriving at the truth (and, of course, either can go wrong). And either can be rational. Take first a case in which you're wondering about whether to donate to Oxfam or to a charity that involves sponsoring a child in the developing world. Both look worth while to you, but you then (perhaps by intuition!) decide that what really matters is preventing as much suffering as possible. You find out that Oxfam is significantly more effective than the sponsorship charity, so you conclude that you'll send a cheque to them. Sometimes, though, rational argument seems unnecessary. You're on the way to meet a friend at the cinema, when someone crashes their bicycle on the other side of the street. There's no one else around. Sure, rational argument might be possible. You might try to weigh the various consequences of assisting the other person against those of continuing on your way, and draw a few conclusions while the cyclist groans softly in the background. Much more likely, however, is that you'll just see the need to help and do what you can. As Bernard Williams once put it, 'The significance of the immediate should not be underestimated'. Which is the wiser strategy -- to follow what you call logic, or what you call intuition? Surely a mixed one, with what is appropriate in each case depending on the situation you're in and your own capacities.
Other things being equal, perhaps we might. But of course they're not equal. Our social morality -- the morality we live by -- is 'speciesist' in the sense that human beings -- whatever their mental or physical capacities -- are considered to be due special protection. If we were to seek to remove that protection, chances are that it would probably degrade our ethical sensitivities to the point that things went overall worse for non-human animals than they do at present. What we should be asking, rather than your question, is: Why should we continue testing drugs and cosmetics on non-humans to the extent we do, when we wouldn't dream of carrying out such testing on human beings with similar capacities?
Perhaps it depends on how strongly you condemn it. Let's assume that, like many people, you think the invasion of Iraq was a crime under international law, as well as extremely harmful and dangerous. Seems to me that we might want to encourage a public morality according to which people who think this and don't speak out should be considered at least somewhat guilty by association compared with those who do.
An interesting question, and one that has received some -- though surprisingly little -- attention in philosophical ethics (e.g. in discussions about civil disobedience or whistle-blowing). I'm not sure, however, that there is really an 'ethics of anonymity', as if that is something autonomous or independent of some normative ethical view or other. You mention 'the right to anonymity', for example. Some philosophers (most famously Jeremy Bentham, who described rights as 'nonsense' and natural rights as 'nonsense upon stilts) don't believe that we have any rights. Others will say that we do, but there's a great deal of disagreement about which ones. For what it's worth, I suspect that in many areas of life where issues of anonymity arise, there are, or should be, codes of practice governing when anonymity is justified, and that these codes of practice should be based on advancing the well-being of all sentient beings, impartially considered.
As you'll have noticed from the responses by Peter and Thomas, philosophers can suggest different ways of defining 'morality'. So here's another one, which owes a good deal to the British empiricist tradition, and J.S. Mill in particular. Morality can be seen as a system of social control analogous to positive law, though its sanctions are different from those of law. Legal institutions will punish you with, for example, some financial penalty, or a period of detention. Moral institutions punish you with blame, shame, guilt, and so on. (This is not to say, of course, that there isn't much more -- and a more positive side -- to both the law and morality.) So what is meant by a moral reason in some society is a reason which you may be morally punished for not acting on. Here's an example. Some action might have the property of being the sadistic killing of an innocent person. Actions like that will meet with the moral sanctions, so that means the property in question gives us a moral reason. Now, could an action be both moral, in this sense, and selfish? I suspect not, since 'selfish' is itself a morally charged quality. To call an action selfish, that is to say, is to criticize or blame it.
Many philosophers -- including Immanuel Kant -- have believed that each of us a duty to fulfil our talents. Often the view emerges out of a religious world view in which we are here to serve some divine purpose and are, in some sense, under the command of, or even owned by, God. Modern liberal views tend to involve something like John Stuart Mill's liberty principle, according to which no coercion -- legal, moral, or social -- is to be applied to others on the ground that it will benefit the coerced themselves. That raises the question whether the kind of person you are describing -- who *suffers* for their art -- will in fact be made better off if they are motivated to develop their talents through guilt, shame, or fear of the opprobrium of others. In many cases, of course, moral pressure won't work anyway. But what about a case in which the lives of others won't go as well if the talented individual gives up on her project? Isn't a potential Mozart obliged to use their gift to benefit others? Perhaps, in highly exceptional cases. But even if Mozart had decided to spend his life bowling and playing billiards, there would have been plenty of excellent music for people to enjoy. There's also a question about whether anyone in the developed world has any aesthetic obligations when there is so much serious suffering which could be alleviated and which might be thought to have a significantly stronger moral claim even on the highly talented.