How many girls can perform in each event?
In the qualifying round (Sunday), four girls perform in each event, and the lowest score is dropped. This allows some room for error if someone falls, stumbles, etc.
In the team finals, only three girls compete on each event, and ALL the scores count. There is no safety net.
In the event finals, two girls per country can compete per apparatus if they qualify.
In the all-around final, two girls per country can compete if they qualify.
Who performed for each event?
For team USA, the qualifying break-down (out of order) was:
Vault: Raisman, Douglas, Wieber, Maroney
Uneven bars: Raisman, Douglas, Wieber, Ross
Beam: Raisman, Douglas, Wieber, Ross
Floor: Ross, Douglas, Wieber, Raisman
For the team finals, the break-down is:
Vault: Wieber, Douglas, Maroney
Uneven bars: Wieber, Ross, Douglas
Beam: Ross, Douglas, Raisman
Floor: Douglas, Wieber, Raisman
Additionally, Raisman will compete in beam and floor event finals, Wieber in floor, Douglas in uneven bars and beam, and Maroney in vault.
These choices take advantages of all the girls' strengths and weaknesses. Maroney is amazing at vault, but her teammates are better at other events. Uneven bars is Raisman's weakest event, meaning she won't compete there in team finals, but she has great beam and vault routines - she qualified for both event finals. Ross shores up the weak points by performing on uneven bars, where she is very, very good, but the team is overall weak. Wieber and Douglas are both proven great all-around competitors, subbed out only where they are weakest.
What were the requirements for the girls going into the All-Around competition?
They have to put up a score in every event during the qualifying round, because that's what all-around is. Those scores are combined for each gymnast and ranked to determine who goes to the finals. It's hard to be an all-around and not an event specialist. Speaking from the team perspective, that limits how many girls can try for the final, because in the interests of the team, sometimes people have to be subbed out (as in the case of Maroney competing exclusively on vault and preventing Kyla Ross from attempting all-around).
Why did McKayla Maroney do the vault twice?
Because you have to vault twice with two different vaults to qualify for vault event finals. This is exclusive to the vault; no other event requires individual competitors to perform twice. The reasoning for this probably stems from the fact that vault is so quick - it's over in a matter of seconds. By contrast, all the other apparatus are longer "routines" where you can show different moves and techniques in a row, which isn't possible in vault. The two vaults have to be from different vault "families," not just variations on the same skill - making it difficult to compete in vault event finals. Other apparatuses don't have this requirements; this is why Gabby Douglas did not do her uneven bars routine twice.
What else is the fifth girl up to?
For the USA, neither McKayla Maroney nor Kyla Ross competed for all around. Maroney in particular is there as what the sport calls an "event specialist" - literally, she is so damn amazing at vault that that is the major reason for her presence. She will compete exclusively on vault, both for the team final and the event final. And the rest is simply cheering on her teammates. If the USA wins team gold, Maroney's vault will be a huge part of that - her scores help make the USA simply untouchable on that apparatus.
Likewise, Ross is there to cover particular events. She has a great uneven bars routine, and that is the weakest spot in the USA gymnastics wall. It's very common for a team to have a few all-around solid girls and a few girls who are spectacularly good at one or two events.
Did Marta Karolyi want Jordyn Wieber to go last on floor?
Let me be clear that I'm not sure if this is true or not, and I'll look. But this is possible because it is an advantage - you know exactly what kind of score you need to put up. Aly Raisman had that advantage instead, and look what it got her. I could actually see Marta putting Aly first instead because she is team captain and had the biggest potential for a floor routine. Instead, it ended the qualifying round for the girls, and they went out well. But it might also have given Jordyn the edge she needed to get into the all-around final.
Overall, the USA's game plan in the qualifying round was to qualify for team finals, where they are favorites for gold. This wasn't particularly difficult for them, and there is room for improvement on all apparatuses, save perhaps vault. Other than that, they wanted to put out high scores to qualify for the all-around and the events finals, which they also did successfully. The finals were great fun to watch.