An air carrier pilot reported they descended below their assigned altitude and below the Minimum Vectoring Altitude.

Narrative

While on an arrival and approach to ZZZ Runway XX an altitude deviation occurred in a degraded situational awareness position; leading to inadequate terrain clearance. The preceding portion of the flight was uneventful other then a late departure out of the ZZZ1 sort; auto throttles being MELd and a large frontal convective system stretching northwards. These benign issues lead to a higher then normal cruise work load. As we neared ZZZ we were given descend via the ZZZZZX arrival. During the flight the RNAV Y XX from ZZZZZ1 had been loaded. This left the bottom altitude of 8000 at ZZZZZ2 in reverse video. During the arrival I asked the pilot flying (PF) if he would like the altitude of 8800 at ZZZZZ3 on the approach deleted. A short discussion about being a higher restriction and the avionics system obeying the higher restriction leading to the inverse video of the 8000 ensued. It was agreed to delete the altitude at ZZZZZ3. Then the PF stated lets just ask for direct ZZZZZ1 for the full approach; to which I requested with ATC. We were given the clearance direct ZZZZZ1 for the RNAV Y XX; descend and maintain 8000. After activating direct I asked the PF if he wanted the altitude of 8800 reentered at ZZZZZ3. Again a short discussion ensued and we agreed to not reenter the 8800 at ZZZZZ3 As we continued our descent and neared ZZZZZ1 we were given cross ZZZZZ1 at or above 8000 cleared for the RNAV Y XX approach. While still in NAV; LAND mode was armed and a discussion about setting the FAF altitude was had but not entered as we had yet to cross ZZZZZ1. Very shortly; as we crossed ZZZZZ1 the Autopilot kicked off and a descent inadvertently continued and confusion about the Autopilot disconnect and approach segment altitude ensued. As I looked up from the Instrument panel we were approximately 7400 feet descending and I called and pointed terrain ahead. At nearly the same time ATC called low altitude alert check your altitude; minimum vectoring altitude 8000. With the Autopilot and auto throttles already disconnected power and pitch were added to climb back to 8000. As that was occurring we got a single EGPWS terrain annunciation. We continued a climb above 8000 and once the terrain ahead was adequately cleared we started back down to which confusion about which fix and altitude we were able to go to. Briefly the aircraft descended to 7800 feet before returning to 8000 and the Autopilot was reengaged; continuing the approach to stabilized criteria and a normal landing. Upon review it was realized that arming LAND outside of 15nm and above 5000 AFE was most likely the cause of the Autopilot disconnect. It was also revealed that the fixes ZZZZZ3 and ZZZZZ4 being similar sounding may have caused confusion. With my previous experience flying the avionics in another airframe; we always deleted out any fixes and altitudes on an approach that would cause an arrival to have a reverse video altitude. This way we wouldn't be predisposed to asking for direct one of those fixes. Also if given direct one of the fixes by ATC that caused the reverse video on the arrival we always made sure to reenter any intermediate fixes and altitudes so that the aircraft would remain on the VNAV Path. Lastly we would never arm the approach or LAND mode until on the final approach course and descending to the FAF altitude in VNAV. These procedures may bring greater SA and alleviate this situation from happening to other crews.