Are the frames of most old pictures in art museums the original ones or were they just something the museum found that would fit?

Frames are actually a very important thing in art. Often for old paintings, the frames are worth more than the painting itself. Wherever possible, the original frames are used as part of the artwork.

It depends.

Sometimes the artist designed or at least chose the frame

Sometimes the original art studio that sold the painting for the artist provided the frame

Sometimes the first owner put on their own frame

Sometimes the museum you see it in decided to reframe the painting

No idea, I would assume that most are antique