These are profound questions and I am sure people will refer you to other postings and useful resources. Just a tiny preliminary comment for you though; Non-self is a key factor here. You're asking "is there still ME when I die?" and, in a way, what a Buddhist would say is "there is no ME while you live either". Conceptions of rebirth vary alot across traditions, but as I understand it, a common ground is the idea that there is no "you", there is a flow of mindstates that follow one after the other, that are caused one after the other, always evolving and changing, and each next mindstate will continue to cause a new mindstate regardless of death. We, our consciousness, will continue to receive experiences throughout.
In Buddhism you let go of the idea of a fixed "me", and rather accept that you evolve over time, each next moment you've turned into something new, caused by the previous moment, both in the physical world and mentally.