House of M was a result of the scarlet witch rewriting reality. Just about everyone was given what they truly desired out of life- spider man was a celebrity, wolverine had all his memories restored, mutants were part of a stable society led by magneto, etc etc. It wasn't foolproof though and eventually some people gained their original memories back.
When scarlet witch reversed it, "no more mutants" was a consequence, since she blamed them for all the things that had gone wrong. Countless millions of mutants had their powers wiped out, leaving only about 200 left, and no new mutant children being born. Who kept their powers was random, since scarlet witch is powerful, but not omnipotent and with questionable control over her abilities.
Quicksilver was also depowered back to human, and gained (new, different) abilities by exposing himself to the terrigen mists- which is a substance the Inhumans (a different earth based race, not human and not mutant) expose themselves to to gain powers. Since the crystals from the mists were embedded in his body for reasons i can't recall, touching former mutants could give them their abilities back, but this was unpredictable and unstable.
But the bottom line is that the REAL reason all of that happened is that there were simply too many mutants in the marvel universe thanks to lazy writers- the purpose of the Xmen made less and less sense the more mutants there were and it was causing editorial problems.
no, since SBP can't affect reality on his own. the "time barrier" he was damaging that caused all those retcons was set up (and not by him) at the end of the original Crisis back in the 80s. Earth-2 superman smashed right through it with 1 hit (clearly being more powerful), so I'm not sure why SBP gets the credit for that one.
