Prophet Adam

God's Emissaries: Adam to Jesus by Shaykh Rizwan Arastu is a nice work on the history of the prophets, according to narrations.

While there are many books of hadith, here are a couple suggestions:

Sunni hadith: 40 hadith by Imam al-Nawawi
Shi'i hadith: The Scale of Wisdom: A Compendium of Shi'i Hadith, compiled by M. Rayshahri

Happy reading!

Islam itself does not require certain beliefs about scientific matters, as long as one's scientific beliefs are compatible with the Qur'an.

The Qur'an speaks about the creation of Adam from clay. Many Muslims take that in a literal sense (Allah fashioned Adam from clay the way a person might make a statue).

However, some Muslims understand that verse in a way which is compatible with evolutionary theory, and that Allah used the evolution of species as a means to produce the human being from what was, originally, the earth.

There are some other viewpoints which are somewhat intermediate; for instance, the view that Allah created other homonids through evolution, and then intervened when it came to our forefather Adam to create or change him specifically.

Of course, from a scientific perspective, the theory of evolution as it applies to human beings is also a developing idea and may be revised or replaced in the future.

So, basically, there is no single view on this topic at present, and a Muslim can hold any idea as long as it is compatible with the basic ideas of the Qur'an (for instance, that Allah is the ultimate creator and had some intent behind the creation of Adam), and as long as they are trying to find out what is truest.

Frequently, religious stories, legends, myths, folktales, etc, preserve an older historical memory, even if some of the details change over time, or even if they are written down later. So the most obvious explanation is that, at some time in history, a big flood happened, and also that people share a common understanding of our origin. 

When religious stories are shared cross-culturally, it can also be understood to mean that there was a shared idea of the story that predated those civilizations, the story is somehow archetypal to the human being (like a fear of snakes), or there was shared access to higher spiritual truths. However in the case of the flood, the historical explanation seems most likely - a big flood probably happened and was integrated into communal memory in various ways. 

Yes. 

Qur'an 7:22 says: Thus he [Satan] lured them on through deception. And when they tasted of the tree, their nakedness was exposed to them, and they began to sew together the leaves of the Garden to cover themselves. And their Lord called out to them, “Did I not forbid you from that tree, and tell you that Satan is a manifest enemy unto you?”

Some narrations say that, after this occurred, they sewed together fig leaves to cover themselves.

It is also narrated from Imam al-Sadiq (A), when somoene asked about this verse (so you are not the first person!), that the private parts of Adam and Eve were originally not apparent outwardly, but when they tasted the fruit, they became visible.

God knows best.