You can stick a sanitized thermometer in there. Better yet go to your LHBS and grab a stick on thermometer and slap it on your carboy/bucket.
Your beer will be relatively the same temp as ambient except during the height of fermentation. There is a lot of heat generated during that process...
We listen to a lot of metal when we brew, but on our chill days it's always Roger Clyne & The Peacemakers. Really good southern/americana/I-have-no-idea-how-to-explain-it jams.
You will have less than 2 gallons left when you're done boiling. When I brewed partial mash I would just top up to 5 gallons with cold water at the end with no issues. Plus it makes cooling the wort a breeze.
I had my hydrometer sticking to the side of my tube once and then realized the patio table I had it on wasn't level. I probably had a few too many homebrews that day...
The same thing happened to me, along with the eye dropper. Beer turned out fine, as I imagine all of the silicone stuff just sinks to the bottom with the trub.