@ViperMaul:
1) Yes, it automatically updates.
2) Ingame you will see "BattlEye Client: Initialized" when entering the game (after the map is loaded). Also, there is a BE filter in the multiplayer browser.
@Fangschuss: What it says, BE fails to connect to the BE Master (arma1.battleye.com). For some reason it can't reach that server.
@xhavenx: What is the exact error message? Is it "BattlEye initialization failed"? You need to install BE then (included in the new patch).