A question related to black holes
Answering your first question:


  If I understand it correctly then the black hole is created by
  collapse of a super massive star at the end of its life. This star
  will have a finite mass. Then what leads to the black hole to have
  such massive gravity so that nothing can escape it (because if it was
  a star before with a finite mass then it would also have some finite
  gravity, right)?


You are right that a black hole will have a finite mass that is smaller than that of the massive star that collapsed (some matter is carried off by the supernova). At large distances the gravitational field of this black hole will be no different than that of a star with the same mass.

The difference arises because in a black hole this mass is compressed into a much smaller volume. Consequently, you can get much closer to the concentration of mass, than you would be able to for a star (where the mass is scattered over a relatively large volume). It is here where the gravitational fields can become really "strong" and prevent light from escaping.