From the pics the compressor bolt is missing , so it could either got loose and fell somewhere or it got broken with its thread stuck in the compressor. Compressor bolt usually get loose and while it is loose its vulnerable to breaking coz of vibration from the compressor and on & off jerks.
It may hardly be an hour job and the refrigerant need not to be removed.
Labour charges are OK.
If you have some tools with you, you can do it your self if the broken bolt is slightly visible.
Remove the loose belt or it can slip off and drop somewhere before you get it fixed.