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The check engine light is on because of p0101 and p0500
p0101 indicates a problem with the mass airflow sensor, it is likely bad, but you can also try cleaning it.
p0500 is a vehicle speed input problem.
the abs system is what provides the speed input for the car and for the speedometer so the problem lies in this system.
the fact that your abs light is on also means that there is a fault in the abs system (and this fault is what is causing the p0500 code and the speedometer problem).
There are two very common things that cause the abs light, a faulty wheel speed sensor or a failure within the ABS / traction control module itself.
You will need to have the fault memory read from the car using a scan tool that can access the abs system (an obd2 tool cannot read directly from the abs system) to determine exactly what your issue is. If a wheel speed sensor is determined to be the problem, then you will need to replace that sensor (about $150 - not $30).
If the module is determined to be the problem, then the module itself will need to be replaced or sent out to be fixed. Two good places that fix these are Module Masters and BBA Reman. You can find both on google. They charge about $300 to repair one of these modules. Replacing the module with a new one will cost around $1000, so sending yours out to be rebuilt is the best option should the module turn out to be the failed component.
Again, you will need to have the fault memory read from the abs system to confirm 100%, but chances are the problem is either a wheel speed sensor or the abs/traction control module.
Please be sure to drive carefully as you do not have ABS or traction control functionality on your vehicle if these lights are on.
As for the mould in the headlight, it will need to be replaced, the seal is compromised letting moisture in. I would consider looking for a used replacement for both headlights.
As for the transmission, I would have the fluid checked and fault memory read out. There are also software updates available from BMW that may help. It may be though that the transmission has been neglected and is in need of an overhaul or replacement.
as long as you get the check engine light off (so address the abs problem to cure p0500 and the mass airflow sensor problem to cure p0101) then the car should pass smog.
I hope that is helpful, please let me know if you have further questions, or if I can clarify anything for you.
It has been my pleasure to help today and I wish you the best of luck with the vehicle.
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