能 is ability, 可能 is a possibility. 會 is grasp, understand, be good at sth, maybe, ability. sometimes, they are exchangeable. of course, every word has many meanings, so you need to judge its meaning through a whole sentence.

Wow that's a big question. So basically能and会are about ability,可以is about possibility，会normally means something that you learned after you were born, like dancing, driving and speaking Chinese.