Transmission issues/double speed/LCM (3.0i)

[terribleperson]

Hello guys,

First of all, I'd like to thank anyone that answers all those questions around this forum, I've been reading on it for couple of months now and resolved tons of issues myself.

So, it's a 2000th x5 3.0i 231hp with GM transmission. When I initially bought it, the clutch was slipping, but the car in general had an engine failure so I bought 2nd hand replacement for both, engine + clutch (I could not find a new one with under 3 weeks of delivery where I live) (https://prnt.sc/uqdw8h). Changed both. Then replaced the whole front with the facelift (don't know if this is important) + put 22" wheels + removed the air suspension to put a normal suspension (reason was mainly because it was beyond repairable). After tons of issues with everything and countless DTCs that I went through I am "this" close to make it run fine again. But I am left with 3 issues for which I can not find information nor I have any more ideas of what could cause it.


1. Double speed on speedometer: This one is odd, because it's completly stable, the arrow does NOT jump around nor anything else, but driving 40km/h (gps speed~) it shows about 75-80km/h on speedometer. Used every calculator for tires and wheels I could find, at worst it should be -1.3km/h with the tires I run, but for me it shows double instead. Had a faulty ABS wheel speed sensor, replaced, no difference. Not a single DTC that could point with a problem related to this.

2. Transmission won't engage : Whenever I have fully stopped or I switch gears I always have to give it a little throttle to about 1200-300 rpm for the gears to "lock" so it starts moving. When it's in D/R without pushing any throttle its barely moving if it moves at all. (I am soon to take it to a transmission mechanic, but I'd love to hear ideas what could be wrong)

3. LCM / relay issue (High beams permanently ON) : I had this problem since I bought the car. The high beams will just go crazy at some point and they do NOT turn ON only when the switch is either to OFF position or to first on to the right. Was told to replace steering column, which I did, it fixed the issue for about 2 weeks or so and then there it is again. (Steering column example: https://prnt.sc/uqe5ec)

The car became a restoration project pretty much, despite it being just 20 years old. I apologize if I explained something wrong or not using the proper terms.

Thanks in advance to everyone who read this!