Will an active duty soldier still receive BAH and BAS after a divorce?

1. Is housing (or barracks) available on post?
2. Does the command know (sometimes they don't) of the divorce?
3. Alimony is not subsidized by the US Military but dependent child support is supported. Does this apply?
4. The Army will try hard not to hurt soldiers but has the lease ended + how long does it have to run?

At a minimum, you will be bumped down to the "No dependent" rate. Will you be able to afford the rent?
Breaking the lease is normally a lot easier than most think. You may have to sacrifice your deposit, but they cannot force you to stay and pay rent. . If your command decides to move you back on post they should guide you on how to terminate the lease.
Talk to your NCOs. Chances are they will get you lined out with no problems.

This would depend entirely on the chain of command and the Housing Authority. Some Housing Authority rules with down town renters have clauses that cover divorce with a lease agreement. Check with your COC and House Authority.