Ok can answer some of your questions as I am currently using my VA Benefits at a Part 141 school. To your first question, yes you can use your housing allowance (aka BAH) on anything you want, including tuition, as the money is deposited directly into your bank account. To your second question, no, your benefits will not pay for all of your exam and checkride fees. It will not pays up to the annual cap (a little over $14k). Pro tip, if you are still active duty, in the reserves, or national guard, you can save yourself almost $1000 by taking all 6 of your written exams in a military testing facility. Not all military testing facilities offer it but most Air Force bases should as well as any Navy or Army base that has a huge fix or rotary wing presence. If you go to a Part 141, your annual cap will be eaten up quickly, so I personally don’t plan on using any of it for the exams or checkride but just for plane rentals and instruction.
Furthermore, you must be a FULL TIME student in order to get BAH. I haven’t gone to ATP, but from what I gathered, it’s probably not going to be possible to be a full time college student and be enrolled at ATP full time.
So your options are basically go to a Part 141 and get about $14.5k per academic year and get ZERO BAH or go to a college program that has a flight school (ex. Auburn University or The University of North Dakota) or partners with a flight school but don’t have a school themselves (ex. Liberty University or Green River Community College in WA state). If you go with the college option, the annual cap is close to $25k for tuition plus BAH. The negative is it will almost certainly take longer than going for the straight Part 141. I considered it but I already have a degree and I’m in 34 now so I opted for the quicker, less benefit route. I basically pay the flight school as I go with a credit card (great for earning airline miles), the VA pays the flight school, and and finally the flight school reissues the check in my name.
Take a look at the link below, it actually gets into pretty good detail about you GI Bill benefits. Let me know if you have any other questions after reading it.