Below is a snapshot of running tthe MCLZ8 at the command-line. It would be easy to add this to the hardware version so you could set a breakpoint, then go into single-step mode which would dump registers, flags, and anything else of interest.
True. I have done this, and was thinking of trying different ROMs on my Model III for fun. One could also make some testing code which exercises all of the TRS-80 motherboard components from the Z80 CPU's slot. I have done this already for the Commodore 64: COMMODORE 64 TESTER USING MCL64
Yes, I use the USB UART supplied by the Teensy and use the Arduino Serial.xxx function calls.
Easily done.. Just a UART keystroke or an access to specific address could cause the MCLZ8 to stop the emulation, dump the CPU state and any memory ranges you wish.