As an operator, not an engineer, I can say the following about the TCAS systems I've used:
1. Pilot can modify display slightly to bias from neutral (normally +/-4000 feet) to "above" (normally +8000/-2000) or "below" (normally +2000/-8000). Software for Traffic Advisory (TA) and Resolution Advisory (RA) is not affected by the display bias. Different systems have different numbers to the above.
2. Uses transponder information, but exactly how I tried to quickly forget. If other aircraft does not have active transponder, you'll see/hear nothing. If other aircraft has transponder, but no mode-S (don't ask I don't want to remember specifics of that) you _may_ see the traffic but will never get an RA.
3. TCAS produces Traffic ADVISORY and Resolution ADVISORY information. There is no _required_ action per FAR, but every company I know about requires following RA unless visual contact is made and/or following RA would possibly endanger the aircraft greater. i.e. descend RA's below 1000'AFL = not good.
4. Most of the bugs seem to have been worked out, but I still see the occasional phantom target, descend RA at low altitude, etc. Worst problem I think is the system's lack of knowledge of pilot/controller intentions. i.e. contact is climbing rapidly to 10,000' clearance altitude and you're at 11,000' (everyday occurance at DFW).