Now that I have all I need, I first decided to connect everything and see if it worked or not. Because my next move is to analyze what's going on between the RAC adapter and my air conditioner, I made a simple breakout board for easy debugging.

And here is my full setup, ready for a test:

After setting up the DIP switches according to the manual, performing a factory reset of the central station and waiting 10 long minutes for that station to finally boot up here is the result.