Sounds like you may have two problems.

Try this. Disconnect the water level tube from the tub and start the machine (you will get some water spilling out so be prepared). While it is filling blow into the tube. If the wter level switch clicks but the water does not shut off the timer is probably the problem. Try replacing it.

As far as the sudden stop is concerned, you may have a brake or brake spring problem there, which is a repair that requires special tools and some detailed instructions. This is a dry brake operation and no oil or grease should come into contact with the brakes.