This is a continuation of my answers to Michael Egnor's Eight Questions for the New Atheists.
5) Why do we have subjective experience, and not merely objective existence?
I suspect that Egnor is referring to the "Hard Problem of Consciousness." I think the Hard Problem can be solved fairly easily. Our brains are information-processing units. "Qualia" (a name for types of internal experiences that we have) are identical to perception, and perception is merely the process of our brains correctly reacting to incoming information. Here's a quote from an essay by Evan Louis Sheehan that illuminates the issue:
"Suppose an alien were to declare that “the hard problem” is determining what it is about those printed slips of paper that gives them their intrinsic value. Indeed, the value of pleasure may be no more difficult to understand than the value of a dollar. Just as a dollar has value only because we believe it has value, I’ll argue that a feeling of pleasure also has value only because we believe it has value. This simple realization allows us to model consciousness as merely a system of beliefs, and beliefs are easy to implement computationally.
"While we cannot imagine how to program a computer to feel pleasure, we can easily program a computer to have a belief system, and we can easily install a belief in pleasure that becomes true when certain circuits are active. We cannot understand how a thermostat could possibly feel cold, but we can easily understand how a computerized thermostat could hold a belief that it feels cold.
"We may easily validate this simple idea by realizing that one cannot feel pain without believing that one feels pain. And neither can one believe one feels pain without actually feeling it. It seems that a feeling of pain and a belief in the feeling of pain are intimately associated, if not identical. Consider also that a hypnotist can sometimes eliminate one’s feeling of pain by simply installing a countervailing belief. And consider that a psychosomatic pain can result from a simple belief in illness. It is even true that a psychosomatic pain can be reduced by a simple belief in the effectiveness of a pill that is in fact just a placebo."
I'd also like to point out that it is not as intuitive as you think to suggest that a physically functioning human being might be able to lack inner experience (somehow).
One author suggests a thought experiment in which we imagine someone who can see/hear/smell (in the sense that their sensory organs can take respond to sound/light/odor and their brain can register information from those organs) but has no inner experience of what it is like to see/hear/smell:
"You wake up one morning, open your eyes, and what do you notice first? That the sun is streaming in the window, that your alarm clock says 7:30, and that your partner is already getting dressed on the other side of the room — or that, despite registering all this in a moment, you can’t actually see anything? Or try a more radical variant, one that takes us a step back towards full zombiehood. You wake up one morning to find that all of your sensory modalities have blanked out subjectively (though you’re still getting all the information alright). Again, what do you notice first: the sunlight, the sounds of birdsong and of traffic in the distance, the smell of coffee brewing — or the total absence of sensory qualia?"
It's just not feasible to think that humans could lack internal experience, not even from a materialist point of view.
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?
I'm not sure exactly how to interpret this question, but the best way I know how is to interpret it this way: How can you have mental states (like thoughts) about others things (your dog, your car, the weather, etc)? A thought is basically just a reminder, inquiry, observation, etc. that comes to your conscious stream. Thoughts are ultimately information exhanges inside the brain that are normally there to affect decision making. And sometimes those information exchanges are exchanging information that is intended to represent facts about one particular thing (and that is what it means for a thought to be 'about' something).
7) Does Moral Law exist in itself, or is it an artifact of nature (natural selection, etc.)?
The 'Moral Law' is an artifact of nature. If there were no sentient beings in the universe, there would be no moral facts in the universe, because morality is a set of abstractions concerning how we should behave if we value other sentient beings.
8) Why is there evil?
The universe is indifferent to human pain and suffering, and so as luck has it some events will lead to the suffering and death of sentient beings like humans.