I have had the modem without power (for example, during power outages, which can sometimes be extended) and there haven't been any issues at all when the power comes back. The modem just picks back up, and if there were updates pushed while it was off, it will get them when it's back on.
I have all of my equipment, including my HughesNet modem, plugged into a surge protected power strip, and I shut the strip off when I'm done for the day. Actually, I unplug the strip, too, though whether I really need to do that is debatable. I've always done so, since day one.
Other than having devices that require 24/7 net access, the only time one really needs to leave their modem plugged in is when they're having some type of HughesNet issue. The reason for this is that the modem logs a lot of information when it is powered, and unplugging it wipes those logs out. When trying to troubleshoot an issue the logs are beneficial to the reps/engineers, which they can see through remote diagnostics. Under normal circumstances, though, unplugging the modem is absolutely fine.
Regarding your first question, some WiFi devices may require manual reconnection to the modem's WiFi after power up, but the modem itself requires no kind of setup or anything. As for your second question, there are no concerns with using this as a form of data control, but, of course, if you do have a data issue it will probably return when the modem is back on, as nearly all data issues are tied to the devices themselves, not the HughesNet equipment.
Regarding the data problem you mentioned, it may very well be tied to the Sonos Speakers. They do keep in touch with the Sonos servers to keep software and lists up to date, and if there is any type of range issue with the WiFi it can cause dropped data packets, which can greatly increase the amount of data being used.
One thing you can try is, over a few hours while you're there, see if there is unusual data usage while the speakers aren't being actively used, and if there is, disconnect them from the HughesNet WiFi to see if it stops. If it does, you'll at least know where the problem lies, and knowing is half of the battle.