Ok...BF2 and BF2142 are really multi-player games. Playing single player is just kind of like practice. The only time your stats will be affected is when you play in Multi-player mode and on a "ranked" server.
The gameplay style of the battlefield series does not have "levels" that you complete. Its strictly multiplayer and you win by bringing your opponent down to zero tickets. Its about capturing flags.
I don't play 2142 so I can't speak for it, but heres the info on BF2.
Play on a ranked server for awhile and acquire some points. After 100 points you will be able to check your stats online
HERE.
HERE is a list of the ranking system and at which points you rank up.
As for why you can't see servers in the multi-player menu it might be because you need to patch up to the most recent version. In BF2 the current version is 1.41.