First Officer reported AIR/GND FAIL and REV ENG 1-2 DISAGREE EICAS message on take off. The flight crew elected to perform an air turn back and precautionary landing at departure airport.

Narrative

After a normal takeoff roll and gear retraction at approximately 400 ft. AGL we had a LG AIR/GRD FAIL and ENG1-2 REV DISAGREE messages on our EICAS. The gear was showing up and locked and N1 remained at the takeoff power setting. We advised Departure that we wanted to level off at 12;000 ft. to troubleshoot a mechanical issue but that we were not requesting priority handling as the aircraft was flying normally. After running through the QRH and advising Dispatch we decided to return to ZZZ. After briefing the Flight Attendant and the passengers we were below max landing weight so we got radar vectors back to ZZZ. We put the gear down at about 5;000 ft. just to ensure we had plenty of time to verify that it went down correctly; which it did. Putting the gear down also cleared both EICAS messages so we were confident the aircraft would handle normally on landing; however we still briefed not to use the thrust reverses just in case. As we were given a heading to join the localizer for [Runway] XXL on a visual approach when the PF (Pilot Flying) armed LNAV to capture the extended center line in pink needles we got an AUTOPILOT FAIL and AUTO TRIM FAIL messages on our EICAS. The PF began hand flying the aircraft and lost approximately 250 ft. in altitude before climbing back to 3;000 ft. AMSL. As we were on a fairly long final as the PM (Pilot Monitoring) I had time to run the QRH for both of the new messages; and decided that we should continue the approach. The PF trim on the control column was working normally. The PF then completed a normal landing and we taxied to the gate. As a crew we worked really well together to divide the tasks at hand and ensure someone was always flying the aircraft. Having completed similar exercises in the SIM we were well prepared for what had happened.