Why and how is a quantum computer faster than a regular computer?
A quantum computer by itself isn't faster. Instead, it has a different model of computation. In this model, there are algorithms for certain (not all!) problems, which are asymptotically faster than the fastest possible (or fastest known, for some problems) classical algorithms.

I recommend reading The Limits of Quantum by Scott Aaronson: it's a short popular article explaining just what we can expect from quantum computers.