From the "Cisco Nexus 5000 Series Hardware Installation Guide", I see that for 5010 model switches, "the chassis supports hot swapping of the expansion modules." This makes me think that if the switch was booted up with a module in place and it then had issues, then I can pull the module out and replace it.
What about a running switch that does not current have an expansion module installed? Can I simply insert an N5K-M1600 6-port SFP+ module and have it show up in the "show run" output, or does the switch need to be powered off, module inserted and switch rebooted?
I think your assumption is correct as the documents say:
"The chassis supports hot swapping of the expansion modules"
Which means any expansion module is hot swappable.
But I would still do it in a maintenance window just in case something goes wrong.
Yes, the module was detected after it was inserted. We removed the filler plate, inserted the module, saw a couple of log messages on the console, ran "show run" and saw the new module ports listed in the output.
We did not have to reboot the switches.