Back to my answering Michael Egnor's "Eight Questions for Atheists":
2. What caused the universe?
The universe has no cause. See my original post for more on this.
3. Why is there regularity (law) in nature?
At the quantum level things don't behave lawfully: sometimes one thing happens, sometimes another thing happens. Human beings only see things that result from millions of quantum events. The basic result brought about by large numbers of chance events is more predictable than any single chance event alone is. Casinos know this. What happens when any one person sits down to play is largely unpredictable. They may very well win some money. They may very well lose some money. But when thousands of people sit down to play, the casino knows the end result. And that's why we observe regularity in the universe.
4) Of the Four Causes in nature proposed by Aristotle (material, formal, efficient, and final), which of them are real? Do final causes exist?
Having had a look at the Wikipedia article, I will answer according to the definitions given there. All of these causes are real in many, though perhaps not all, situations. The final cause of a thing (ie its purpose) exists only when there is an agent who has made the thing with some purpose in mind, or when an agent uses something to achieve some goal. Things which are not made by an agent can't really be said to have a purpose unless an agent uses them for a purpose. Rocks don't have purpose unless someone uses them as a paper weight, or as something else. I was not created with a purpose, however, I can use my body and mind (which are ME) to achieve happiness in life, which is my goal. And that means that I have purpose.