Air Carrier First Officer reported while on the final approach segment; automation mismanagement caused an altitude deviation; receiving an altitude alert warning from ATC and setting off a EGPWS configuration alert. The pilot stated the autopilot had been disconnected to increase the descent rate and was not reengaged. There was also a distraction of a similar call sign with the adjacent aircraft on a parallel runway.

Narrative

We were cleared by ATC to descend via the ZZZZZ 5 RNAV arrival and to expect an FMS XXR using the autopilot in VNAV. They then cleared us to descend to 6000 ft. after crossing the ZZZZZ waypoint at 7000. The airplane descended to 7000 in VNAV but I had to do LVL CHG to get it to descend to 6000. I did not re-engage VNAV since we were not cleared for the approach at that time. Immediately before reaching ZZZZZ1; ATC cleared us for the FMS XXR. There was an added distraction with a similar call sign; the other aircraft was landing on a parallel runway. PM (Pilot Monitoring) set TDZE but I did not re-engage VNAV. The aircraft began a slow descent out of 6000. ATC issued a low altitude warning at approximately 2000 ft. before ZZZZZ2. I disconnected the autopilot and the TOO LOW FLAPS warning sounded since we were not fully configured at that point due the distraction (flaps 15 with gear down). We quickly configured and continued the visual approach to a safe and normal landing. The conditions were VFR and we had the runway in sight at all times.