If it only hums, the motor isn't able to rotate. First disconnect the driveshaft and try to run the motor. If it runs, the pump is bound up/clogged. If the motor continues to hum, the bearing is shot. Repair or replace motor. Good luck.
Yes.
Install a new filter
Sure
Absolutely. Many people excacate and then place an above ground pool into the hole such that a foot or two stays above ground. Also make sure you either have clearance for your filter system or run the line into the ground and up to the filter as well.
Probably not going to be adequate.
It should be on "FILTER"
Probably not going to be adequate.
Attempting to obtain step by step diagrams connecting an above ground pool to a sand filter.
about an inch below the TOP of the filter...there should be a line on your filter...
no.
YES it should be no problem
Proper water chemistry instead of neglect. Long filter periods and a clean filter.