The symptoms of agitating while filling and the extra water at end of spin point to a bad auto load sensing switch. This is a high failure item on this washer. I would first check the hose that runs from this switch to the air dome on the lower right rear quadrant of the outer tub. If the hose is loose/split/cracked, it can leak water and cause the switch to not operate properly. Normally, the air dome and hose present an airtight seal. As the water level in the tub increases it compresses the air in the dome and hose and the switch monitors this pressure to determine water level. Also, make sure there is no gunk buildup in the air dome and hose. If it checks out ok, I would replace the switch and look for the leak elsewhere.

Eric