How long will I have in the barracks to collect BAH after getting E-6?

A barracks clearance memo is required in the packet to start your BAH. You can not live in the barracks and collect BAH at the same time. Better start saving your first and last months rent. There is AER if you need it.

That depends on your base and your leadership. I got promoted to SSG a month before I had to PCS. I asked the BN CSM if I could just stay in the barracks until I left. He said sure. (This was in 2009). But I didn't apply for BAH until I PCSed to my next unit so I wasn't pulling any BAH until a month or two after I got promoted.

This will depend on your installation. Most installations require that you vacate the barracks once you have attained the rank of SSG. You will receive BAH back pay from the date of promotion or the date you move out. Normal protocol is that if you are living in the barracks, as single, you will not receive BAH. If you cannot afford the initial move costs, contact ACS for financial assistance. In the future, as a SSG you should be aware of the value of saving money. You should have been saving some money since this seems that you were aware that you would eventually be moving out of the barracks.