Best Answer: Hi, 'see you' is just a way of saying goodbye, one that has become 'fashionable' to use.
1) See you later, exactly what it says, is an expression used by someone who is leaving, but will see the other person later. Or, it is used, once again, 'fashionably' just as another way of saying goodbye. Lots of people say this to me, and we have no arrangements to meet. It used to fox me at first, but I realised its just the 'in' way to say goodbye :)
2) See you next week - with no prior appointments. Never heard that used casually, but only when people meet every week, for example a club meeting every Sunday, when they leave the meeting they could use that expression, knowing that they will meet again next week.
3) I'll be seeing you ....just means that the person leaving is assuring the other person that he/she will see them again. It can be said with pleasure, or even menacingly by someone who is kinda placing a threat over someone else, for example someone in 'Godfather' could say that to an enemy who on the face of it is a friend....but he knows that the other person knows he is his enemy, and he doesn't really want to see him again, lol, hope thats not too confusing!
4) I'll see you when I see you...this is just an expression that says the person does not know when he/she will see the person he is talking to again. Could be tomorrow, next week, next month, next year even. So, no, just 'see you' would not suffice in this instance.
Hope this helped :)