When someone practices a difficult song or does exercises and their fingers get sore, does this mean they are getting stronger/faster/all round better
Yeah, it's called callouses. That's good, the more you practice the more it'll happen till eventually you wont feel it anymore
Well, your fingers have muscles/tendons and crap in them, so it's basically like working out at the gym. You play enough to work those muscles and they start to get sore. That usually means that the muscles are becoming exhausted and thus will stretch, making them stronger, etc.

Unless they're sore 'cause you've dropped your guitar on them many times...
Yeah, these guys are pretty much all right. Soreness is normal when your first starting out and your fingers are just getting used to the strange things you do to them when playing guitar.