Car smoking with burning smell

What is your question?

I have a 2009 Mitsubishi Galant I drive it daily when I first crank it up it makes a noise twice like it doesn't want to start then it finally cranks up mechanic check out the battery and alternator said both was fine suggest that I try a starter so I order a starter mechanic put it in then the car starts to make a louder noise then before and it's smoking and has a burning smell so I park it at home next day I try to crank the car up it wouldn't start and it's making studdering noise so I had to get a jump off for it to crank up took it back now the mechanic saids my battery is bad but I don't think it's the battery not when he just test the battery and alternator and said they both were fine and I don't think a bad battery causes a car to smoke or have a burning smell I think it's the new starter so what could it be?