This you could get away with for awhile without further damage. Motor mounts have a built in safety device to keep the engine in place when the rubber mount breaks.
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If you rev your motor and the motor moves excessively one or both of your motor mounts is broken. Visual inspection is the best method for determining the condition of your mounts. Jack up the car and put it on jack stands. Get underneath and look at each of the mounts. The rubber should not be cracked or missing pieces. Push on the motor with your hand and make sure the rubber is not broken and that both sides ( motor and the part of the chasis where it mounts ) are firmly attached.
Typically age/wear. If you replace one, you should consider replacing all of them as they are weakened by the bad one.
Could be a bad starter drive or a broken tooth on flywheel/converter Try turning motor manually (make sure it is in neutral if std.) by using a large socket on the crankshaft. If starter works this way probably a bad tooth if not, probably a bad starter drive
Blown fuse, bad heater blower motor control switch, bad blower motor, or a bad blower motor resistor pack.
either the control head is bad or there is a blower motor resistor that is bad.