A319 pilot flying reported the aircraft did not level off on the glidepath of the STAR and the approach; even though everything looked to be set up properly. ATC issued a low altitude alert and the aircraft issued an obstacle alert.

Narrative

Starting on the ZZZZZ STAR we first noticed the airplane descending below an altitude constraint at ZZZZZ1. Aircraft descended to 12800 ft. before I caught it and leveled off. ZZZZZ1 is 16000 - 13000. No explanation as to why the airplane didn't respect the STAR altitudes. Next; ZZZ turned the airport around and gave us vectors off the arrival and told us to set up for Runway XX. We requested the RNAV RNP XX and set up and verified the approach. Everything looked correctly set up. We were vectored around and cleared the approach when I depressed the approach button and confirmed all correct indications. APP NAV and stick and a brick." The airplane started descending but wouldn't level off at the appropriate constraint. Tower called us with a low altitude alert at which time I turned off the autopilot and hand-flew the altitudes. At no time we're near restricted airspace. Again the indication was trying to get us to descend and we received an "obstacle alert." We still have no idea what the RNAV was trying to do as it was set up correctly. At this point; we noticed it dropped out a point on the arrival and the approach mode was off. Upon hand-flying and descending to the proper altitudes on the arrival; we broke out at 1000 ft. and we landed normally.Cause: Bad weather. Last-minute runway way change. RNAV confusion and possible malfunction. New FO (First Officer) with 140 hours.Suggestion: Go around and figure it out."