1993 Nissan Maxima heater core or blower (fan) + 1

I have a '93 Nissan Maxima GXE with 150k on the engine. I'm having two current issues. First, when the car is running a smoke will emit from the defrost vents causing the window to fog up. I still get hot air and this fog goes away after the car runs for long enough. I heard this is probably the heater core or fan? Ideas? Second, because of this fog/smoke problem I had my car parked all winter on a hill. When I went to move the car this spring the rear wheels were stuck. Locked ebrake? Somethin' else? Thank you so much for your time and insight into how I might go about fixing it.