The best thing about jumping into a long-running series is the joy of discovery. You have all the wonderful back-history to unravel, and your enjoyment of the current issues increases as you start to understand what happened in the past and see the way creators integrate and change characters in the present.
Science fiction isn't really about the plausibility of the setting, but more about the effects and opportunities that radical discoveries might have on humanity. Traveling faster than the speed of light is unfathomable according to modern science and technology, but it is a necessity if you want a story where humans meet aliens from outer space.
Fiction, according to Neil Gaiman, is inherently lies.
It used to be that mutants were defined as those who developed powers while going through puberty, not necessarily those who are just born with powers. Franklin Richards was born with powers, but isn't really thought of as a mutant.
These days the X-Books aren't all that picky about membership.
If it concerns you that much, just skip the movies and read only the comic books. The films are not meant to be an affirmation of our collecting hobby, it's just Hollywood cashing in on an existing property and using the comic fans to help fuel their hype machine.
Anything important with Iron Man or Batman or Spider-Man will always happen in the comics. Remember when Warner Bros told DC that Superman couldn't get married in the comics before he got married on TV? You know what they did? DC killed Superman. For weeks, everyone forgot that Lois and Clark was even on.