u/BeginningAd3008

Hey there all, very new here. About 5 months ago I picked up this E93 325i with the N53. Lately there’s been quite a few engine related issues. I am led to believe this is the High pressure pump about to die but i want to be sure before I rip the whole engine to pieces. The codes I get are 0029E1 for dme mixture control occasionally one for fuel pressure plausiblility but that ones rare. I know the NOx sensor is dead. The car runs very rough on idle but smoothens out. I had a code yesterday for a missfire on cylinder 1 that soon went away. The car loves to misfire at idle when cold. Even more so when the HVAC is on. It hesitates and jerks a lot under heavy acceleration in higher gears. Please help!!