B757 Captain reported autopilot failure and left thrust reverser failure during descent for landing.

Narrative

On descent for landing; the autopilot operating on the left autopilot due to the center autopilot out of service; we were cleared to 14;000. It was extremely busy due to numerous thunderstorms in the area; causing numerous aircraft to deviate and were going to alternate locations. We were also deviating to try to avoid the thunderstorms; and dealing with the FO's headset working intermittently. We got the alert of altitude deviation and the aircraft had descended below 14;000 feet by approximately 300 feet when I pulled the yoke to pull it back up to 14;000 feet quickly. Nothing was said by ATC about the deviation. We confirmed the correct altitude was selected and releasing the yoke; it tried to descend again. I disconnected the autopilot and then was given a lower altitude. I reengaged the left autopilot and needless to say; watched it carefully. It worked normally until we were cleared to join the localizer at which time; while joining the localizer; it disconnected; and the approach was hand flown. To continue the problems; upon landing; the left thrust reverser failed to deploy. When describing the situations with the mechanic; he mentioned that he had read up on the aircraft before we arrived and said it was the same reason that the center A/P was MELd out of service.