You would need 1" diameter rings with a height of roughly 1".
The scope rings on the BSA Sweet 22 6-18x40 mm will not have a set-pin in the scope rings, which would be needed to mount onto an air rifle, we would recommend using the BSA Outlook Series, which is designed for air rifles.
Most scopes can. At the range, I sight my rifles in at 50 yards, and put a mark on the turret. I have never had a problem doing this. IF you have a problem, then you can take a piece of cardboard, and peel off the sheet off the TOP or bottom of the cardboard exposing the corrugated material. Then use the thin piece of cardboard that you peeled off (not the corrugated piece), and put it between the scope, and ring, on the rear mount. This will raise the back just a tad, and this is how I saw my rangemaster adjust my friends cheap scope that would not go down/up enough.
No, it does not.
This has 35 MOA of adjustment each for both windage and elevation.