Welcome..
I would guess that the misting problem is due to a leak in the heater core or the rubber seals. I had the same problem when I bought my car(except it was summer so I didn't notice misting). In my case the coolant would leak out slowly, so it may be that you haven't noticed it yet. Be advised that sometimes the coolant can leak out onto the carpet of the car so keep an eye on this. Do a search, there are many postings on replacing the heater core(I did it in August); its a bitch to get to, and even more of a bitch to remove and install, but certainly doable with patience.
As far as the blower, I suspect that like me your resistor pack is gone. On LHD cars it sits up behind the pedal cluster and is a simple remove and replace. Older E34's had a sword resistor for climate control- not ours.
I can't help you much on the first point of constant heat, although I suspect that some valve that allows coolant into the core for heat is stuck open. Either that or the control isn't working to close it.
Hope this helps, and good luck.