I think all your problems are tied to one cause. Check your drain hose going to the wall, if it is too far down the pipe you will get siphoning and will cause the above symptoms. put the drain hose down the pipe no more than a foot and report back.

You have two problems. First, you may have a bad water valve, and second, you have a bad lid switch. I would replace both items. Water valve AP2046012, lid switch AP2045986
Before replacing the water valve, I would check for soap residue in the bottom of the tub where the plastic hose going to the water level switch is connected. If there is residue I usually add some vinegar in the tub, wait for a period, then blow in the plastic tube to clear it out, or you can use a funnel to dump vinegar down the plastic hose.

Follow the plastic line from the water level switch down to the plastic bowl at the bottom of the tub. Check that bowl for soap residue!