Just a couple of things I noticed when flying. There was one time on startup where both EGT's went up to max upon introducing fuel. I got ECAM warnings for that as well. It hasn't happened ever since though so I'm not sure if I did something wrong that time or not. Also I was attempting to use the Airbus throttles instead of the Boeing ones since I like them better, and when I was calibrating reverse thrust would always activate no matter where I calibrate idle thrust. I also tried calibrating idle reverse lower than where it actually should be to create a buffer but that didn't work either. I changed to the Boeing throttles and did not have any issue probably because reverse isn't on the axis for that throttle.

The first issue sounds like a hot start, that happens when fuel is introduced too early into the engines.

As for the TCA issue, look here: