Christian Hannah

Chosen answer: As revealed in the post-credits scene, he transferred his consciousness to another body, one without brain function, just before his own was destroyed. He foreshadows this during a lecture early in the film, when he talks about the mind living on even when the body dies. So his mind, his "self", survived, even if his physical form did not. It is widely assumed among X-Men fans that Charles transferred his mind into his comatose twin brother, thereby explaining how Charles later looked and sounded exactly like he did before Jean disintegrated him.

Answer: It is shown in X-Men: Days of Future Past that Hank made a serum that can help him walk.

Chosen answer: The short answer is events in this film negate what happened in X-Men 3 as well as Origins: Wolverine or one could say this film essentially became a reboot. Since no real answer seems to be given, and since the X-Men 3 film makers didn't know Charles would later be shown to become paralyzed prior to visiting Jean, they had no need to explain why he's walking. One can only speculate on the possible ways Charles walks in these 2 previous movies (and this isn't taking into account the timeline shift from X-Men Days of Future Past). We do know from DOFP that Hank/Beast created a serum for Charles that allowed him to walk, albeit without his powers. Hank could have kept working on this serum which would allow Charles to walk and still maintain some of his powers. Then at some point Charles stopped taking the serum, confining him to the wheelchair once again. Either because they ran out of the serum or because Charles came to the realization he needs to accept what happened and not hide it, especially if he's teaching children to accept who they are. Charles also has the power of "astral projection" and the power to appear in the minds of others, so Charles could simply not be there at Jean's house, but is back home, in his wheelchair.

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