-Chapter 65 pretty much tells you what the Ackerman family(re read it again) were before they started killing them. They are also seem to be super human, how and why will be answer soon. It's already been teased with Levi, Mikasa and Kenny's when in struggle for the first time. They are feared because of their power and their counter to the erase of the memories.
-The full power to be only for a member of the Reiss family is tricky, because it turns out to be true then Eren's is dead, someone will eat him or another Reiss will turn up soo, maybe the Ape? who knows.
-As for the basement it can be a combination of many things, antidote, the truth about the outside, the titans, the walls build from Titans etc.