This washer starts to work properly. The tub fills and the agitator rotates during the wash cycle as expected. Then the pump drains the tub, but it never spins. Instead the agitator continues to rotate during spin cycle. Is this a thrust bearing issue?

After the spin cycle ends and the rinse cycle starts, the tub does not refill with water and the agitator does not move. About 1/3 through the rinse cycle the timer stops moving, and I can hear a soft hum until I unplug the power or press the timer dial to turn it off. Is this a timer issue?