Yes, TCAS RAs are only in the vertical plane.
If an aircraft is at its service ceiling, this can be taken into account by TCAS which can be "climb inhibited".
In the scenario described by I-FICO there are three possible outcomes depending on which aircraft declares an RA first and the Mode S addresses of the two aircraft.
1. Own aircraft stays level (told not to descend) and the other aircaft descends.
2. Own aircraft told to descend and the other aircraft climbs...
3. ...unless the other aircraft is also climb inhibited, in which case own aircraft descends and the other aircraft stays level.