Alternator belt wouldnt cause any of these problems, basically you slacken the tensioner off, take the old belt off, new belt on, tension the err tensioner and re-tighten.

I hate Garages, I wouldnt trust leaving my car with them


I cant think of anything they would of touched doing that lot that could cuse your car to run funny? Check all plugs are on/properly, all hoses are tight, even the breather-metering unit. .all I can think of really