Do I need to face my new frame? I just purchased a new aluminum MTB frame. The headset is a standard "NECO, 142, 1-1/8” AHEAD". The BB is ... I'm not sure, but is internal and threaded.

How do I determine if I need to face or ream my new frame, before pressing in headset cups and installing the BB?
If your bottom bracket is a sealed cartridge unit it's less important.  If you're using a bottom bracket that has loose ball bearings and a spindle it's very important.  Mostly the same advice goes for headsets.  All this is less important than back in the day when all BBs and headsets had exposed and floating bearings inside.