TCAS is always active if your transponder mode dial is in such a position, so it always calls out other aircraft that are nearby and could pose a threat of mid-air collision. However, resolution advisories are inhibited near the ground. The last thing you want to be telling a pilot to do is to increase their descent when they're only a thousand feet above terrain -- this would at the very least trigger a more serious GPWS callout, the response to which is drilled into pilots during training -- pull up, directly into the path of the thing TCAS would want you to avoid. If the other aircraft also has TCAS equipped and enabled, and their RAs aren't inhibited, they will still get a climb instruction (both crews usually get opposite instructions in order to maximise the vertical separation).

Correct. At that altitude TCAS RAs were almost certainly inhibited. They might have gotten a TA.

On the tapes, the military helicopter was warned about the airliner. They replied that they had the traffic in sight and requested to maintain visual separation.