Should I try to repair an A/C condensate pump that has suddenly started getting real noisy?
Replace it.  They are cheaply made and the little motor's bearings can wear out.  They are much cheaper to replace than the cost of the damage that might occur if it fails and floods an area of your home.

As for maintenance, I would open it once or twice a year to check/clean slime out of it so it does not clog.  After you clean out slime, pour a watering can full of water into the auxiliary inlet (the hole plugged with a blue cap) to verify that it pumps the way it should.