When you lock with the AIM-120 selected, it does change to STT lock.
LTWS is a work in progress. This has been stated many times and in great detail.
This is not a feature that exists in the real aircraft. You can switch to flood mode after the missile is fired, but you would have to do it manually.
This may be a bug. i have not tested it specifically, but AACQ was working for me the other night.
For something like this, you need to provide a track. There are many variables that come into play when talking about accuracy and missile failures. It's entirely possible that you broke lock before the missile went active.
Work in progress.
IFF and radar identification are both works in progress. There IS in fact rudimentary IFF, but it's unreliable at best.