Lately it seems to take longer for my water well tank to fill up - almost six minutes compared to a few years ago when it seemed to take only about 2 minutes?

Also when I use my washing machine - the water well tank empties and it takes a few minutes before the water well pump clicks on? What could be the problem?

Check the little tube between the tank and the pressure switch. Probably clogged. Assuming you have bladder tank, check the little air valve on top. Should have air coming out not water.