1) TCAS RA's are a coordinated response between two conflicting aircraft. The TCAS units actually talk to each other and agree a course of action.
Just to nitpick but RAs are not always coordinated. Coordinated RAs may happen if
both aircraft are TCAS II equipped. But there are plenty of aircraft without TCAS II (and perhaps only Mode C/S).
If the other aircraft doesn't have TCAS II, an uncoordinated RA may be generated. That means there's a higher chance that the other pilot might make a conflicting evasive maneuver. Bottom line is to always be prepared for additional RAs (reversals, etc.)