I'd go see a new mechanic. Heavy vibrations could be either misfires, rough running, or motor/trans mounts and if he can't diagnose those, you need to find someone better.
Auto stop start is consistent for me, either not happening or happening due to battery power, outside temp, etc.
Smoke is likely fluids on the exhaust manifold, very common to have oil leaks out of engine cover gasket or broken engine cover.
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