Does science leave room for "free will"?
I would say yes. We all have first hand empirical evidence regarding the existence of free will, since in our everyday lives we are faced with a large number of choices to take. Then I'm not sure specifically what 'science' would say, but perhaps cause-effect, etc etc, therefore our choices are an illusion. To me it's just not conclusive enough, but if you framed the question by saying the question by saying 'Science has absolutely destroyed the concept of free will', then I would say no, so clearly some room must be left for it, not matter how slight that room may be.
Does man have a "soul," separate from Nature, that is "responsible" for his actions? When, in the 14 billion year history of the Universe, did this "soul" arise?
If by that you mean a non-physical entity, or something to that extent, I don't believe in a non-physical world due to lack of evidence. It's possible but, even if it were true, we have 0 understanding about this non-physical world so your latter question is impossible to answer.
Do animals have "free will"?
If you think free-will is derived from mans faculty of reason, and you agree that certain animals have at least this faculty to a far lesser extent, then it wouldn't be unreasonable to say that they have free will, but to a lesser extent. This question kind of requires a definition of free will.
To what extent is legal and moral responsibility justified and to what extent is it an outgrowth of our primitive desires for retribution and vengeance?
The real question is, if someones reprehensible actions are entirely out of their control, should they still be held accountable? In any other scenario, the answer would seem no. If Y holds a gun to your head, and tells you to shoot X, to me you really didn't have any other choice, but the responsibility is not on you, but on Y, since they were the ultimate cause of your action. The ultimate cause of your action if you do not have free-will however, can't be attribtued to anyone else this way. You can't say that environmental factors are to blame, as you would be then blaming everyone else, including the victim, but not the person doing the act. So then, what is to blame is your genetics etc. If you accept that you had no control over your actions, but your internal factors are to blame, then you should be held responsible, if for no other reason than the fact you are deterministically immoral, and your existence wouldn't be conducive to the society we want to live in (generally speaking).
How does our nature and nurture factor into our decision making? What about mental defects? Are we responsible for the inner mechanics of our brain?
Cbf discussing.