Currently, Battlefield 3 does not support cross-platform multiplayer.
According to this article, which quotes the studio head, Robert Bach, there are numerous differences between the PC and Console versions of Battlefield 3:
Limitations caused by hardware requirements causes the maximum number of players in a game to vary between versions:
The biggest difference between the PC and console version of Battlefield 3 is that we have 64 players on the PC and 24 players maximum on console...We tried to get more players in [to the console version] but then you need to scale down all the graphics, scale down all the destructibility, and sometimes you need to scale down all the map sizes
Alterations were also done on the maps themselves to make them work better for smaller numbers of players:
When we say they are smaller, it's not that we have cut them in half. But we tried to compact them slightly to keep the action up.
Judging by these differences, and the licensing/requirements mentioned by Stof, it is extremely unlikely that there will be support for such a feature.
On a side note, having such a feature would be a huge win for this game franchise, which is in constant competition with the folks over at Call of Duty, and I'd hope that any game promoter/marketer would have immediately jumped on it as a major selling point if it was a plausible future enhancement.
The best game modes to level up in would be Conquest and Rush.
The reason these two are the best are because they contain objectives that are worth a lot of points.
The fastest is probably conquest as capturing a point (including neutralizing the point first) will net you 450 points (350 for assisting a capture) and there are many many points to cap per round. In addition, if you kill anyone while inside a flag's area of influence, you'll gain an extra 30 points per kill.
Rush is the second best as you can also get 600 points per objective (100 for arming, 500 for destroying. Only 200 for defusing) played, but they're aren't as many, and it's harder to get defends etc.
Best Answer
The ONLY things that you lose for ending a game early are:
Any points/kills/captures etc that you would have received while continuing to play.
The ribbon for whatever gamemode you're playing (including the winners ribbon).
Any end of round only ribbons like MVP or Ace Squad.
It will always count as a loss on your record.
You won't lose any progress that you made during the match, including ribbons, medals or service stars.