Kind of, yes.. There's actually 24p, which is exactly 24 still frames per second, this is what you get with film. Then there's 23.976 which is generally referred to as 24p, but has slightly less frames per second than 24. It actually works out to about 1.5 less frames per minute than 24p.
If I were in a PAL country, as the OP is, I'd probably stick with 25p. Since the power system is 50Hz there, vs the 60Hz here in the states, I believe there'd be less likelihood of weird strobing from lights at 25p in Europe.
That's conjecture, since I'm not in Europe, and haven't shot anything there, but it makes sense that if you shoot 25p, with a 180 degree shutter, your shutter will be open for 1/50th of a second per frame, which would play much nicer with a 50Hz light wavelength than 1/48th of a second per frame. The difference is very minimal though.
You are slightly wrong, yes. Generally speaking, the faster the frame rate, the smoother the motion captured is. However, generally for film, the intended playback rate is going to be 24 frames/second (at least theatrically), so if you were to shoot at a higher frame rate, ideally more than 30 frames/second.. more like 40+, you'd be doing so with the intent of conforming that footage to 24 frames per second, which would then make it slow motion.
Yes, in a manner of speaking, you would capture more detail at a higher framerate, but that's not precisely the intent. Also the difference between 24 and 25 frames per second is negligible. 1 frame per second isn't going to be terribly noticable to most people's eye, and it's still more filmic looking than the NTSC standard of 30 frames/second (or more specifically 29.976 frames per second, or 59.96ish fames per second for 60i footage).
Bascially it works out like this, the higher the frame rate the smoother the motion.. and the higher the playback framerate (30fps vs 24 for example) the more it looks like the 5 o'clock news and the less it looks like a "movie"
That's a big part of the reason that I, for one, think the whole 48fps so-called HFR format that, for example The Hobbit, used is truly dreadful for a filmgoing experience. Aside from some pretty crappy shots in the latest hobbit film (bad compositing and VERY video-looking during the barrel scenes) I'm not too keen on paying $30 for my wife and I to go watch an exciting version of prime time TV on a big screen in a dark room with a bunch of loud people we don't know.