Won't go into drive or reverse

If the vehicle can't go into gear, why can't the dealer check it?
Did you check for trouble codes?
How is the condition of the transmission fluid and its level?

Check out the guide below, it will help you figure out whats going on

https://www.2carpros.com/articles/automatic-transmission-problems

First thing to do is to check if the axle shafts have given way.

Put vehicle in Park and with handbrakes off, try to push the vehicle forward or backwards. It it can move, that would mean the axle shafts have given way.

That means it is not a fault with the drive axles. It is transmission related and could be due to a failed torque c converter, the transmission itself or its control.

Check for trouble codes to see if you come up with anything.

May be CV joint inboard if not then problem in differential

As long as you get the correct trans you shold be ok swapping it out you don't have to do any computer recognition as you aren't replacing the module. If you have done this before then it's pretty much the same on all cars. Check fluid if you can as you may not have any way to check it but with mileage don't be surprised if it's time for a rebuild.

If you are swapping out a trans, the converter should come with it. If it's the pump seal or any outside seals replace them and then lube with Vaseline or KY jelly Make sure your converter is in the pump all the way otherwise if it slips forward it can break the teeth in pump and you'll have to rebuild it. Make sure to use proper fluid or compatible.

The problem could be that the thermostat is stuck open, does the heater work okay?

In older transmissions yes, I do not think they have those in these cars, It could be a speed sensor for the transmission or one of the internal seals is starting to let go and it shows up when it is cold because the seal contracts.

Looking forward to your reply :-)

P0755 - Shift Solenoid B Malfunction
P0760 - Shift Solenoid C Malfunction
P0765 - Shift Solenoid D Malfunction
Code 1529 involves the speed sensor circuit

So you think three parts failed at the same time? It is very doubtful this is a transmission problem. You have to look at what all these things have in common, and that is the computer controller and the wiring.

The way to find out which parts are needed, (if any), is what you pay a mechanic to diagnose. There's no way anyone can do that over a computer. As you've already noticed, diagnostic fault codes never say to replace parts or that they're bad. They only indicate the circuit or system that needs further diagnosis, or the unacceptable operating condition. There are entire books just for troubleshooting these codes.

The "How To" guide you're looking for is the service manual. Don't waste your money for something like this on Haynes or Chiltons manuals. Those only cover things experienced do-it-yourselfers can handle. You need a copy of the manufacturer's service manual, and their Transmission specialty manual if it is a separate manual. In the Transmission section, you'll find a few hundred pages of information, mostly on diagnosing mechanical problems, and rebuilding procedures, torque specs, line drawings, and special tools needed. There will be pages detailing how to replace the speed sensor and shift solenoids, but usually not information on how to diagnose them, ... Usually. That is left up to the individual systems manuals.

I don't mean to sound like a spoil-sport, but the fastest, least expensive, and most effective way to solve whatever problem you're having is to get a mechanic involved. It sounds like you think removing, disassembling, and repairing an automatic transmission is a simple task, but in fact, less than one or two percent of mechanics specialize in this area. All the rest of us can do is remove and replace them. This is a highly-technical and very specialized field, and you only want someone with plenty of experience tearing your transmission apart.

As an alternative to the service manual, you can go to the top of this page, point to "Service and Repair", then click on "Manuals" to be taken to a page where you can buy a subscription for your vehicle. It will include most of what is in the manufacturer's service manuals, and there will be places where other people have posted what they found to solve various fault codes. That's where I found the speed sensor was replaced for code 1529. Solutions for codes 760 and 765 weren't listed.