Is it possible to fly 100 kilometers with a propeller driven aircraft? and if not what is the limit of a propeller driven aircraft?
The altitude 100 km is also known as the Kármán line. It is also called the 'edge of space'. No aircraft can fly higher than this line. Because of the sparseness of the atmosphere they would have to go so fast in order to generate lift that they would reach orbital velocity. Therefore they would be spacecrafts, and not aircrafts. As you can see it's a theoretical limit, in practice aircraft fly a lot lower than this.
So in effect, no it's not possible for a propeller driven aircraft to fly above 100 kilometers altitude, but this is also true for any other kind of propulsion.
About your other question, I believe it's already answered quite nicely here: How high can propeller airplanes fly?