First, the TRS-80 Model I, Model 3, and Model 4 were largely - but not completely - compatible.
I don't recall all the differences, but slight variations in clock speed, larger differences in boot ROM, and some port addresses (if I recall correctly, one of the larger differences was disk subsystems).
It should be possible to make one core accommodate all of these, but the disk subsystem(s) would probably be the most difficult aspect.
(Model II was a different beast entirely.)
Yes, you have found the official RS-232-C interface document; this should be considered the quintessential version for Model I. It was an add-on to the Expansion Interface. While I recall there were RS-232 interfaces which didn't require the Expansion Interface (I didn't have the EI), they were compatible.
I seem to recall at some point that some people were "hacking" their units to use a 16450 or 16550 UART for better baud rates and/or buffering, but the electrical interface (including port/memory addressing) would have remained the same.
Back at that time, I recall only two main uses for RS-232:
- modem/terminal software (I don't recall a specific package being a leader, but if Radio Shack listed one, that would have been the defacto standard)
- driving a serial printer
At this point in time, the Hayes "AT" command set was not yet established as any sort of standard, so any modem setup was mostly done manually - DIP switches were used (on both sides), not software commands.
It was truly the wild west.