> Since films are shot at 24fps, how were they converted to 25?

Sped up by 4% to make them 25fps. The audio is supposed to be pitch-corrected, but some poorly done conversions did not do that.

Does that mean one of the frames is duplicated every second?

No. If you increase the speed of 24 fps video 4%, it becomes 25 fps. Frame count does not change, frames are just shorter.

Yes. Imagine that you had a fast-forward button that changed the time per frame from 41.7ms to 40ms. This is what a cinema-to-PAL conversion does.

It's a bit weird in the sense that everything is sped up and faster than normal. In the other hand, it's super simple and does not introduce the even weirder judder that a cinema-to-NTSC (telecine) conversion would do.

Personally I think it's easier to get used to everything being slightly faster but unmodified otherwise than to having additional frames being inserted and the resulting judder in all motion.