You aren't in 4WD on hard pack are you?
If the Rhinos are anything like the Grizzly (which they are), the rear end doesn't have a diff in it. It's spooled, so therefore you will get some binding/ jerking on harder packed terrain or pavement. This is normal.
As far as the rear end getting hot...yes it will be pretty warm or even hot after a hard run.
For gear oil for the front and rear end, just use any 80 WT GL4 or better (GL5) oil. It's just gear oil, like the oil in the rear end of trucks. You don't need any special fluid or brand or synthetic, just plain ol gear oil.