Good to hear on the fan fixing the fuse problem. At this point then, it might be a refrigerant issue.
The basic issue on refrigerant is that the system is designed to contain a certain amount of it (by weight), and it is tough to measure how much is in there. Pros have equipment to easily evacuate the whole system, weigh it, and put back in the exact right amount. Without that equipment, the rest of us can only take pressure and temperature measurements and make our best estimates based on those. Not impossible, but not necessarily easy in problem cases, which I think is why you are getting the sound advice to take it to a pro.
I posted something a while ago on freon, which might give a basic understanding of why this pressure issue is not as simple as filling a car tire:
https://xoutpost.com/1166563-post28.html
It's good that you've found you have at least some pressure there. That means you have some refrigerant left, and that positive pressure will have kept contaminants from getting in. If you measure pressure (at the low pressure port, but as
@upallnight said, if the compressor is not running and the system is not blocked, pressure will be equal throughout) and it is below that of a saturated vapor, that means you have only gas in there, no liquid. That might be great in that you'd know the system was almost empty and you could make a good guess about how much to add. Vs. the more common DIY-type approach is to keep adding freon until the pressures are right. That might be fine unless there is something else wrong in the system and you would overfill it, not reach the proper pressures, and have a new problem.
On the fan spinning:
There are 3 wires going to the fan. Two thick ones = +12V power and ground. And one thin one. The thin one is a pulse width modulated 12V square wave coming from the ECU. The duty cycle of that square wave is interpreted by the fan controller circuitry (which is built into the motor - take off the cover and you'll see an epoxy-encased circuit board in there) to set the fan spin rate.
This thread here had a lot of info on exactly when the fan should spin, how it is controlled, etc.
https://xoutpost.com/bmw-sav-forums/...-fan-woes.html
But one very simple comment is that if the fan is spinning, the ECU is commanding it by signaling with that square wave on the control wire. No simple grounding or powering that wire (e.g., with a short or jumper) will make the fan spin, as far as I know.
As discussed in that thread I link above, for example, in post #28, you'll see how one of the things that can trigger the fan to spin is removing the pressure switch. So for example (only!), if that switch is damaged or removed, that might tell the ECU to tell the fan to spin at full speed. And who knows, maybe the PO rigged something to make that happen, to prevent overheating, and running the aux fan all the time burned it out, etc, and your problem has nothing to do with AC at all.
Not that I think all that is the case, but something like that could be. The whole system is pretty complex. There is a lot of inaccurate info out there on the intertubes. So unless you get lucky, you might want to figure out the whole system or take it to a pro. Or try on here; hopefully you can get the info you need.