Welcome to the 'Bolt.
to answer your questions #1-No, the fan shoud not be on with the key off. Most likely the wire is connected to a constant live feed instead of a keyd one.
#2-The signals should self cancel. The cancelling cam is probably worn or bent. Could also be a mis-alignment of the mechanisme in the housing, but that's unlikely. You can get a new cam from any of the parts suppliers, I got one for my '55 from American Classic (see link at top of page).
Don't worry about asking questions if you can't find the answer. If/when you can, post some pix.
