How much time can elapse between users action and a reaction of the application to make the user feel like it was "instant" or "in an unnoticeable time span"? (Some say that 250ms, others say 100ms, whats the real number, approx?)
100ms is correct. Plus/minus something, depends on the user.
This article has a nice picture: http://en.wikipedia.org/wiki/Reaction_time
As you can see, 100ms is the time, a user detects a change, but he needs longer to respond to the change.