How can I pause/resume rsync

You can pause any program by sending it a TSTP (polite) or STOP (forcible) signal. On the terminal you've run rsync in, pressing Ctrl+Z sends TSTP. Resume with the fg or bg command in the terminal or a CONT signal.

It is safe to kill an rsync process and run the whole thing again; it will continue where it left off. It may be a little inefficient, particularly if you haven't passed --partial (included in -P), because rsync will check all files again and process the file it was interrupted on from scratch.

There may be unusual combinations of options that will lead to some files not being synchronized properly, maybe --inplace with something else, but I think no single option will cause this.

If you disconnect your laptop and reconnect it somewhere else, it may get a different IP address. Then the TCP connection used by rsync would be severed, so you'd have to kill it and start again. This can also happen if you suspend your laptop and the TCP connection times out. The timeout will eventually filter out to the application level, but it can take a while. It's safe to press Ctrl+C and run rsync again.

Ctrl+Z to suspend, and:

$ fg

to continue, use

$ jobs

to see suspended jobs; bg [number] to background them; fg [number] to foreground it.

Run rsync with the --partial flag. It will then keep partial transfers and resume partial files when started.