The RF module I am referring to is the one on the WiModem232 itself. That module contains the CPU/RF and serial interface. If that is defective then it could do weird things.
Have you tried using NComm or JRComm? I use these terminal programs. I have not tried any others for the Amiga (other than the 64 door), so I don't know how they need to be setup in order to use a real modem (which is what the WiModem232 emulates exactly).