As for the hinged fin: the 707 had the same feature and I'd be surprised of he 737 didn't have it too. I once saw a Monarch 720 outside their old black hangar at Luton, (northernmost corner of the apron, besides the Britannia ops block. Both gone now I believe) the 720's fin was folded flat on top of the right hand stabiliser in order to get it in the hangar.
A folding vertical stabilizer sounds like an accident waiting to happen ...
Does anyone have a photo of one ?