Should it work? Likely. But you will have to see to find out. Some people have reported problems in the past using eSATA drives that also have Firewire ports. It depends on the controller on the inside. I tried a spare Vantech USB/Firewire/eSata I had lying around many many years ago to no avail, but the non-Firewire model worked fine with the drive (that enclosure/HD combo has been working now for 5 years or so on an 8300HD).
As for the second question, if you want to turn your external off, you need to first do a hard power off of the unit (so pull power from wall), turn off external, plug the unit back in. Then when you want the external back on, you need to hard power off the unit, turn the external on, then power back up the unit (yes you can also do it off a reboot but this is the safe way of doing it). Obviously when the external is unplugged your PVR will only record to the internal drive. This isn't a recommended way of doing things. Once you attach an external, you should just keep it attached and on at all times. Then you don't have to worry about missed recordings or corrupting your index file.
Also, get yourself a UPS for both the PVR and the external, so you won't have problems with power outages. It doesn't have to be a APC 2200 VA or anything (its for sure overkill on my 8642HD), a little 300 or 500 VA unit that you can get for like $50+ at BB, FS, Source or wherever will suffice (as I use on my 8300HD).