Can't figure out how to replace these MR16 GU5.3 bulbs
The MU16 connectors are a twist type, turn counterclockwise to remove. They often need some effort to turn. There isn't anything physically stopping it from turning other than 
friction

The buzzing is either from a dimmer, a bad bulb or electromagnetic (EM) interference. Remove the dimmer if there is one. Verify that the bulb is good. Test for EM interference from other devices by turning off devices in the home until you find the offending item. 



Picture: lightbulbwholesaler.com