If you have other questions, just add them with a replay and they will be added here. ;)
Q: What's a League?
Leagues are the way players are divided and organized when they decided to start playing into the competitive multiplayer Ladder of Starcraft II. We have 7 different rank for now: Bronze, Silver, Gold, Platinum, Diamond, Master and GrandMaster. Each game mode (1v1, 2v2, 3v3, 4v4) has separate and different Leagues (only GrandMaster is exclusively for 1v1). Initially you need to make 5 qualifying matches before being assigned to a league. Leagues are only linked to game mode and not to the race you play.
1v1: after five qualifying matches we are assigned to Platinum. We have played always using Zerg, now we want to try Protoss. We'll not have to do again qualification for 1v1, we'll stay where we are. We can play every race we want.
2v2 (it also applies to 3v3 and 4v4): we do qualification with a friend and we qualify in the Gold League. The day after, I want to do another 2v2, but my friend is not online, so I select 2v2 mode. I'll play that game with one random ally, selected by matchmaking system, but I'll have to do again 5 qualifying matches. I can play in the first Gold League only when I'm in group with that specific friend. Different friends, different Leagues.
Q: What's a Division?
Once we are assigned to a league we'll not have a general ranking, we'll be put inside a Division with other 99 players. There are a lot of Divisions inside each Leagues, and they are here to give a more close and realistic objective for every player: reach the top of that not so big group. Winning matches will let you gain points (depending on the strength of your opponent) that will allow you to advance inside your division.
Q: Are names of Divisions unique? How are they generated?
They are generated in a random way, not totally random, but at least a part of it. No information for now if those names can appear at same time in different leagues or they are totally unique.
-Suggested by Antoxa-
Q: Where will I be promoted to an upper league?
Only one factor count: your victories, it's not important how you win. No matter what's you position inside your Division (you don't need to be first). Periodically, the matchmaking system will let you fight versus "Favored" opponents. Winning this, and other match, will help. If your performance is very good you could also be promoted directly from Bronze to Gold (for example), jumping over Silver.
Q: Can I also be demoted?
Yes, as you can go up, you can also go down. Active Player population in SC2 is divided equally in each Leagues, 20% for each rank (only Master is 2%, Diamond 18% and GrandMaster is the top200 of an entire region). We cannot be all in Diamond or Master, otherwise the entire game would lose its meaning. ;)
Q: Will my league change if I'm away from SC2 for a while?
No, your league will never change if you don't play. It is possible that when you finish your first match (after your return) you could be put into a new league, but this is something rare.
-Suggested by Raiju-
Q: I've seen the profile of some of my opponents (in 2v2, 3v3, 4v4 mode) and I noticed that they were much stronger than me. I'm bronze and I'm getting diamonds as opponents. Is this normal?
When you look a player profile you see his best leagues, because that is what is displayed. He might have been in a bronze league team when he was playing with you.
The other explanation for this is that you have been very successful in your last games, and the system decided to test your strength versus tougher opponents. You'll lose very little points if you play versus much higher level players, but you'll gain a lot if you win.
-Suggested by Zee-
Q: Why sometimes do you see your opponent "Favored" when match start and when it finishes it said that he was only "Slightly Favored"?
At the moment there are no official information available about this. We don't know how the system decides who is "Favored" or why there are sometimes this kind of discrepancy.
-Suggested by Rael-
Q: Inside Leagues, is it random to be in one division or in another?
The system try to put players with similar skill inside same division, of course this is not always possible for logistic reasons.
-Suggested by Woland-
Q: Is it possible to play two ladder games in a row against the same opponent?
Yes. The ladder system doesn't eliminate any player who was assigned to clash with you even if he has just played a match with you.
-Suggested by Hyouma-