For example VFR can be used in not at busy airports to land faster (visually) as you don't need to fly published approach.
Maybe GPWS was activated by unstable approach? Too big descent rate ect. I think it can be also activated if you are with gear down, low and not near airport. It depends how the modern system is.
If rudder trim is 0 rudder is centered. If you set it to non zero aircraft will turn left of right.
TCAS uses special logic when the aircraft is near or on the ground. For example it will not issue descent RA when you are near the ground.