What is the routine maintenance you should perform on your brushless motor after a day of racing or practicing?

Nothing, just make sure its not overheating and not getting alot of dirt in/on it.

No bearing drops or anything like that?

The bearings on BL motors don't need mantenace as often as brushed motors. You should check the bearings once in awhile but not after every race. Also a lot depends on the can design of the motor as some BL motors don't have any holes for dirt to enter while others do have holes.

It really depends on the manufacturer. Castle recommends that you never oil the bearings in their motors, and they are the only that I know for sure makes a recommendation. But some of my cheaper motors I prefer to oil them every 10 runs or so just to be sure.

Yeah that probably has to do with the type of bearing that's in thier motors. Some bearings are designed to be maintenance free and are lubed for life and don't need to be re-oiled. For example BOCA's Ultra Seal bearings don't need to be re-lubed so if you put those inside a motor then you should have to check the bearings at all.