Exhaust Fan tripping GFCI
First try to stop the nuisance tripping by cleaning out the dust from the fan motor and connection block.

You don't need to have the ceiling fan GFCI protected. You said you have a GFCI receptacle in bathroom so that satisfies the requirement.

You could change the connections of the wires to the GFCI receptacle in the garage so you don't use the load terminals. If this means that some outside receptacles are no longer GFCI protected, then you would have to replace the existing receptacles with GFCI ones.