OK, so you have a 01/2002 E46 M3 Coupé S54 Europe Left hand drive N
It always helps if you tells what car you have - diagnosis on a Z4 is very different to an E38

Anyway that error report tells a lot.

1. MFL error - a static MFL error exists (MFL=Multifuncton steering wheel)
Check power wiring to MFL and to control unit, check slip ring, check button boards in MFL.

2. Brake light switch
A sporadic "Short circuit to battery or value too high" error exists.
Check brake light switch, replace if necessary.
Check wiring loom and connector around brake light switch for chaffing and damage
As brake light switch and MFL are in the same area of the car, check carefully that area for anything out of the ordinary - wiring loom damage etc.

EG: a chaffed wiring loom would explain the electrical burning smell you had.