3 types of headset: Std, semi-integrated(zero stack) and internal.
STD – press fit cups
Semi-integrated – lower stack press fit cups
Internal (integrated) – bearings just sit inside frames
Most MTBs have the top 2 and yes if they are semi-integrated (if that is your setup) the bottom cup can be removed and a 1.5″ fitted for a taper 🙂
A tapered fork won’t work in a non-tapered head tube but vice-versa will
Not quite true – if you have an OS straight head tube you can run a 1 1/8 straight or a 1 1/8 to 1.5 taper