I wiki'd Xavier last night, he's in and out of that wheelchair like a frikkin' yo-yo.

You guys do realize that the movies take place in a different Marvel Universe from the comics, right?

In fact, the comics take place in several different universes, depending on which runs and versions you're looking at.

Comics and superhero universes are like mythologies (Greek, Norse, or otherwise). There is no "canon." You just pick the version you like the best.

Did Zeus decapitate his dad, Cronos? Or did he castrate Cronos? The older versions go with the latter, but we generally teach the former to kids. According to one version of the Medusa story, after she was decapitated, Athena attached Medusa's head to her shield. And thereafter, Medusa and Athena became linked symbolically, and Medusa could even be described as an aspect of Athena. (Hence why Medusa's visage appears on the Parthenon doors.) But most of the stories we keep telling about Athena don't portray her in her terrible Medusa (or Medusa-head-bearing) aspect. Switching over to Norse mythology, there all kinds of different versions of just what the heck Loki is, let alone who he is. (There are very similar problems with the almost identical story of Lucifer/Iblis in Christian and Muslim mythologies. The fact that he is conflated with Satan only muddles things more.)

Some big clues the Wolverine movie is not in the same universe (as if there were only one) as "the comics" are:

1. No yellow spandex.
2. Either less or more violence, depending on which comics you're talking about.
3. Different takes on several characters (including Deadpool).

Yes, I believe Gambit did live out in the swamps in at least some comics story lines. Except that many comics (like many movies) are happy to assume that the city of New Orleans and "out in the swamps" are synonymous. In this movie, at least, he seemed to be living in N.O. (though, I admit, it doesn't specify where he was raised). If it makes you feel better, it was probably hard enough for the casting folks to find someone who looked/felt right (impertinent smirk, roughly the right age/build), let alone someone who looked/felt right who could also do a non-vomit-inducing Cajun accent.

We don't know why or when Xavier became wheelchair-bound in the movie universe.