Regarding your question of TCAS - GPWS coordination, Jofm5, it would be redundant. Radio altitude is a primary sensor for both systems.
There are 3 basic advisories from TCAS: Descend, Climb, and Maintain Altitude. If one of those commands is unwise, such as ground proximity or max altitude, then it selects the best command from what's left.
Air-air coordination between planes in conflict is based on ICAO sequence number assigned to every plane equipped with Mode S transponders. The one with the lower number is in command of the coordination, and the other plane responds as needed.
TCAS, GPWS, and Windshear advisories are prioritized so that only the highest priority is annunciated by lights and audio.
GB