Some are 5v some 7v not sure if there any others but could be 12v ones.

Did you check the voltage on the original plugs.
Had the wrong voltage plugs for my 320d but the plugs looked the same.
My e53 has had all failed plugs for the last 6 years and never failed to start it did have 1 good one 7 years ago lol.

Battery is good then.
Not sure what the problem is.
Does the wiring on the heater look original pr has it been played about with.

I fitted a 9" screen Chinese unit some years ago now and it works well.
One thing you need the long cable that runs to the rear of the car and it connects to the dvd and stuff in the ps cubby hole.

+1 on battery age and condition will stop it working.
???? you open the doors and not start the car ???..

Basically if it didn't come new with them then it's a mot fail that is what the bible say's. If you fitted new lights then you might get away with it but up to the tester on the day. Retired now but was a tester for years and my m8 who test's my cars always ribb's me over my led number plate lights ...

Why park in D and not P.
I never use the handbrake it's pointless.
Same on my MB and that has the exact same setup drum/disc and the adjuster exactly same.

Send Uncle the bill for fixing the rim's.

Have you looked in realoem parts catalog it will show you and give you the correct part number.
Just enter the last 7 of your VIN number.
https://www.realoem.com/

Mine is 22 and gets everything it wants.
My m8 of 45 years has a garage and any noise or anything i hear gets looked at asap.
But at test time i still panic and deep down i know it will pass i was a tester myself for a long time and check my cars all the time.

Might sound daft but you could try the magic reset.
Disconnect the car battery for 20 minutes then put it back it can sometimes sort things out.
If the battery is in the boot DON'T shut it or bonnet as you won't be able to open it with no battery connected.

Hope you didn't take it for a beer.
lol.

9 year old plug's and filter are due a retirement party.

Fronts are easy on bmw cars i have found but the rear ones can be hard going.

Diff windup.
Mixing new and old tyres.