I am left wondering if some vents blow down too forcefully on particular tables in the resturant?

If there was enough time for the pulley edges to wear out the belt - then it is highly likely there was also enough time for the blades of the fan to get dirty.

Those “wandering flames” due to rusted and split tubes ought to be checked out after re-checking what your net loss would be after insurance if the building were to burn down. Imagine how many attorneys would chase the case if someone were injured of killed.