OP, You are fixated on Brown yet you seem not to even know that Brown doesn’t award college credit for AP classes, they are only used for possible placement in higher classes. But that is moot, as everybody has told you that your family will be full pay and it doesn’t seem like your family will do that. I guess my initial point is, you need to research the schools you are looking at, not just assume things.
In regards to your #1, taking that many AP classes can indeed raise your GPA alot, it can also tank it if the workload is too much.