What atheists believe (part 2)

4) Of the Four Causes in nature proposed by Aristotle (material, formal, efficient, and final), which of them are real? Do final causes exist?

Not enough context to give a good answer.

5) Why do we have subjective experience, and not merely objective existence?

We are imperfect beings. Perfection doesn't exist in anything remotely complex. Objective experiences  would require that we process ever input perfectly from all points of view. We simply can't do that, so we are stuck with the alternative. 

6) Why is the human mind intentional, in the technical philosophical sense of aboutness, which is the referral to something besides itself? How can mental states be about something? 

 Question is meaningless to me. If someone will clarify it, I will give it a go...

7) Does Moral Law exist in itself, or is it an artifact of nature (natural selection, etc.)

Morals are simply a sense of fairness. It can be seen in other social mammals. It comes from nature in that treating fellow social members of your unit fairly increases your chances to breed, remain in the group, have your young cared for, etc. 

8) Why is there evil?

If you mean people who do bad things, because some people lack that sense of fairness. We care for all people and their kids. So morality is no longer being selected for in the same sense it would be if our society was under more survival pressure. Again, there is no such thing as perfection in this world.