It does some of them, not all. It does keep some track of the IP, but doesn’t give you a viewer for it. I tracks it for the unique IPs and simultaneous login restrictions. WP Admin > s2Member > Restriction Options
There isn’t a downloads log viewer. s2 keeps track of the unique files the user downloads, but not every time he gets the same file in the period defined for the limits. WP Admin > s2Member > Download Options > Basic
A downloads logger and viewer is something I’ve been thinking about, though. I’m adding your vote for it in my list.
You can define materials per person, using custom capabilities. It’s a bit manual by default, but you could create some simple PHP to automate some/all of it. See: https://www.youtube.com/watch?v=BBltDUopo1U
What do you mean by “access by registration”? That the user has to register to have access? Yes, this is mostly how it works. You get the user to register, and the access is given to his account as the role or capabilities. https://s2member.com/kb-article/s2member-rolescapabilities/
I hope that helps.