When you go to court, inform the judge that he is living downstairs from you, and that it makes you afraid. He's still drinking, and he's a violent drunk. What's to stop him getting angry while he's living downstairs and trying to barge his way into your apartment?
He should NOT be living downstairs from you. Do you have a restraining order/protection from abuse order? Or was there just a "no contact" condition on his bail? If you haven't applied for a restraining order, I strongly suggest that you do that. It's more permanent than a bail condition, and it can also prevent him from living in your immediate vicinity.
And I suggest you contact the prosecutor to find out what's going on with the criminal case. You should have been notified of any court dates.
The alcohol and abuse may be related, but the alcohol does not CAUSE abuse--it just lowers the inhibitions. I also suggest you reach out to your DV shelter or advocacy center, and talk to an advocate about getting some counseling and safety planning. Al-Anon can be a great help as well.
You CAN heal from this, but you must keep yourself safe in the meantime.
Hugs,