"Bookworm, if you have an old transponder which only supports mode A, will TCAS react to it?"
Yes, it will. It will assume that the other aircraft is at the same level and play safe by giving an alert against it. This is a problem because the pilot of the TCAS equipped aircraft gets the alert but does not know whether to look up, down, or level! It is not a good idea to rely on azimuth avoidance because the equipment is unreliable around the 12 o'clock position. A mistakenly applied 'avoidance' turn could put the two aircraft on a collision course, rather than into safety.
Which is why, if a transponder has Mode C/Alt facility, it is better for that mode to be selected, rather than just plain vanilla mode A.