Is it really a ss? YES!
This is a totally acceptable way to rig a SS. The purists and fashion police may laugh at you, but you don't care, right?
I ran that setup for a while as SS, and it worked fine.
If you want to finally get rid of the kludge factor of the rear gear cluster, I would just pick the gear you like, and screw on a BMX freewheel. The threading is the same, and you can get them in sizes 16-20t in both 1/8" and 3/32" chain. There is really no need to redish. With 126mm rear spacing the freewheel isn't
that far out of alignment. I ran my SS setup like this for almost 2 years, I never redished. The only reson why I changed it was because I loctited on a track cog in place of the BMX freewheel. The chainline is still slightly effed, but I haven't had a problem yet in the few months I've been fixed on this bike.
So a redish isn't really necessary, but it will make things run a little smoother and quieter.
A QR rear works great, provided you use an old steel QR, have serated steel locknut faces, and have steel dropouts. I used a QR rear for SS, and currently use a QR rear for fixed, and never have had a problem or a wheel slip. Much more convienent, IMO.
Here's a pic of my old setup from the winter: