BMW Repair: abs light and speedometer, rear wheel speed, bmw e36

Question
few days ago I bought a BMW e36 318tis compact with m42
engine. It had a bad engine which  I repaired and found that
speedometer doesn't work and abs light is always on. I
tested instrument cluster and everything works. could you
ell me what the problem might be? and in addition ambient
outside temperature is minus 40 degree Celsius.

Answer
The easy one first:  The ambient air sensor will read -40 when it's disconnected or bad.  See if it's plugged in, then decide if you want to pay for a new one if it's bad.

For the speedometer and ABS light, the right rear wheel speed sensor (also referred to as the ABS sensor) sends signals for both the ABS and for the speedometer.  Assure that this is plugged in.  It's worth a try replacing it to see if that does it.