NOISY FUEL PUMP ON 650 YAMAHA VSTAR (2002)

if the bike is fuel injected- the pump is in the fuel tank.. if the bike has carburetors- there is normally no fuel pump- the fuel gravity feeds from the tank thru the petcock valve into the carbs

Have you checked the fuel supply? Could be a dead fuel pump or a blocked fuel filter.

If the mechanic did not replace the exhaust pipe gaskets in the head or on any connections between the head pipes and the mufflers , the air leaks could be igniting unburned fuel in the exhaust , causing the popping and back firing. Try replacing any gaskets in the exhaust system.
If you have a flat spot or hesitation when accelerating than you probably also need to rejet the carburetors. Bigger main jets should fix that condition. A jet kit may also contain differently tapered needles for the slides to help compensate for the change in the acceleration curve.

The buzzing is caused by a flat battery. or dirty corroded battery terminals.
If the battery is a few years old and has been sitting for a while it often pays to get a new one.
Running a less than perfect battery and or jump starting may cause other problems as it may overstress the charging system.

Could be the coil. Also could be several other things. Download a shop manual and diagnose it.