Depends on the ship you AA, not all ship you AA on it will make you level faster.

Example, the Ppro1 and Deustchland level far faster than moltke even with higher level crew.

AA is the only way you can earn your own exp as a lower level ship. What it wont do is teach you to play a gunship though.

The IJN BB1 (Kongo) can mount the dual 3inchers which is at least some AA. You can shoot down scouts or inattentive scouts with more hp fighter planes and then you've done some attack so you get more exp

You wont get more exp for your contribution, but you'll get more exp because youll contribute more.

AAing does tend to add more experts to your crew though if you can do it well.

As for your BB, you could just try playing cautiously, waiting back, playing near the mid. If youve not played many GBs then sit back and watch others near the start, see who sinks early and who stays longer. Notice how ships split north and south and tend to sail in a line shooting across at each other. This can also happen in the middle and can be a safer bet for low level BBs. Learn to become aware of wether you can be seen or not, this will become a crucial skill. Try to learn where enemy BBs are and to stay aware of roughly where they are when you can no longer see them so they dont sneak up on you from the darkness.

And consider getting a PBB, they generally perform better than the BB1 and 2 and are a useful boosters for early GB play.