When firmware updates do eventually roll out, do I have to restart my router or does it automatically update and restart when it receives the update?
I'm currently waiting for the latest update to come out so that it will fix problems with my Galaxy S7 but I don't really want to be restarting the router every couple of days in anticipation of this update.
It will sort itself automatically if left to its own devices. You may be able to trigger a "manual" update with a restart, but probably only by a few days because firmware roll outs are phased by area (and possibly even within area).
Depends how desperate you are for the fix, but my suggestion is wait it out and let it happen automatically.