2 is certainly out. Procedural rules oblige AA to answer.

To 1: Whether DOT takes action, and when, is uncertain. Some of the complaints I filed have been pending for well over a year, I believe some as long as two full years. Now, DOT is busy. And since DOT prefers to settle these cases, not litigate them, there can be an odd negotiation -- DOT wants a tough settlement; airline says "what are you going to do about it?"; and they're a bit stuck. This may look like "DOT ignores" the complaint although I don't think that's the best assessment in general.

3 is perfectly common -- airlines often try to buy off complainants with individual benefits on condition of complainant withdrawing a complaint. That's not my game -- I want to get problems fixed for everyone's benefit, not just get one benefit for one person (even myself).

5 is possible. Always an airline's right. No reason why the complainant has to complain about the very best / very lowest fare in the system. A complainant wanting to start in some country that is 5% less than USA would suffice as a matter of law and would still amply demonstrate the problem.

6: I don't know that such a rule is permitted. I'd need to do some legal research, including as to credit card rules, the duties of common carriers, and other sources of authority. My hunch is that it's not permitted or else more airlines would be doing it already and would have done it for years.