Well, the good news is that you have heck of a car. The powerteam on the Z3 is little short of fantastic. It was one of the most flexible combinations I drove in the 90s and early 2000s. It still stands out today.
I agree with you, if there was one still in my driveway, I’d want to keep it, as well. The problem is your two problems. I have to suspect that the rest of the Z3 is fine mechanically and that you are asking about the tranny specifically, of course.
Your first problem is the friction plate. Since you are hearing squealing when you are getting into gear and then cruising, it indicates that the fiction plate (some people call it the pressure plate) is slipping. It is literally sliding against the clutch plate on the engine side. Eventually, the plate or plates will wear out and while you Z3 may start and run, it won’t go anywhere.
Though it is fairly straightforward getting to the pressure plate, you still have to open the transmission housing, remove the transmission itself and then you will have to access the friction plate, remove it, after removing things like the input shaft and such and replace it. It’s not an inconsequential job and will cost you the better part of $2,800, though in some places you may be able to save a bit, maybe $400 or so.
The second part of the problem involves the device that has likely been the cause of the whole problem, the throwout bearing. As you probably know, when you press the clutch in, the linkages exert lifting pressure on the throwout bearing. When that bearing is disengaged, the friction plate disengages and the engine and transmission are free-wheeling because they are no longer connected.
Though the throwout bearing is inexpensive, as transmission parts go, because it costs about $225 or so (maybe more or less, depending on location), replacing it is, again, costly in terms of labor and potentially outboard parts (linkages and such) that may also be worn (this is a big if because standard transmissions are very robust) because you have to remove the transmission from the housing to get to the part. The good thing here, though, is that you will already have the transmission open to replace the friction plate so that you can replace the throwout bearing at the same time. All told, you are looking at a bill of about $3,000 for the work on both parts (this is a BMW, after all).
Good luck and enjoy it when you have it repaired.