So finally, after many days of troubleshooting, this thread can finally come to an end, we have good news! The Switch is finally running functionally, I didnt even get one single freeze since the console has been running for a few hours now!
You see, I tried improvisingly reflowing the mainboard in my cooking oven, which, to be fair might not be the most precise in temperature, but it did the trick. I was following a tutorial on Youtube about reflowing in a regular oven set to 200C or 392F for about 8 Minutes while the mainboard is suspended on rolled up aluminum foil balls. Surely enough, I actually gave up on the idea and cancelled it after about 3 Minutes of reflowing, thinking it would just destroy something. After reinstalling the mainboard the thing just works flawlessly to my surprise. What I really did not expect is the short amout of heat to actually have helped in the end.
So, what can we conclude? It was certainly not the missing resistor, in fact, I have yet to find any function that is not working right because of that missing resistor on pin 2 of the M92T36 chip. The previous owner most probably left the device out in the cold and brought it back inside to warm up very often, or the chip was just not soldered on correctly during manufacturing. The little troublemaker was, as @DeadlyFoez suggested, probably the CPU or if not then the DRAM.
Also, since its not freezing up all the time, the docking function, as well as charging works now as well, and I can even finally see the battery percentage rise or fall live!
Now, of course the oven method, or at least the way I have done it, is not a permanent fix, and in fact, that loose solder joint on one of the chips is going to lose contact sooner or later anyways. But by the time that happens I will either reflow the board the right way or find a professional to do it for me. I might know a little shop nearby that does BGA reflowing as well, we'll see. Anyways, if anyone does ever run into this issue, and people surely will because I can't be the owner of the only switch that has a bad solder connection on the whole world, this thread may serve as a good help to find a solution, like it did for me as well.
I'd like to thank everyone for suggesting how to fix the issue, and for taking their time to help me troubleshoot. I wish I would have tried reflowing earlier, but at least we came to a solution in the end.
I might stick around this forum for longer though, some threads about the switch are rather interesting and people actually contribute to threads.
So, if no further questoins come up, we might consider this thread as closed. Thanks!
Did reflow Xbox 360 the same way. Also this is the way to easily remove an iPad screen from the iPad . Good to hear you fixed it! Now you can enjoy the Switch!