The answer is the you do not put a scope on one.
The model 31 was sold with a JC Higgins scope in the early 1950's and an original scope is going to be pretty hard to find. Any scope for a grooved receiver should fit. The value is principally as a shooter as there does not appear to be significant collector interest. The rifle was manufactured by High Standard although they did not put that model into the High Standard line. The design is very similar to their Sport King rifle although the Sport King is a pump and the model 31 is semi auto. The gun was available with an internal, retracting sling that is pretty slick and in 22 long rifle or 22 S, L, & LR chamberings. Some parts are available through gunpartscorp.com
You can scope just about anything with a bit of creativity and a good gunsmith. Go talk to one. If you can find a scope mount that will work with the configuration of your weapon, then it is down to drilling and tapping for the mount. If you have no idea how to do that, or don't feel comfortable working with decently close tolerances....... Go see a gunsmith.
No - Not correctly
The JC Higgins Model 21 is a pump shotgun, not a rifle. Reassembly should be done by a competent gunsmith.
Yes
Yes.Most marlin model 336 rifles have been drilled and tapped for a scope mount on top of the reciever.
A Marlin model 81 DL is the same rifle. You can put the same stock on your J.C. Higgins. Now to find a stock for a model 81. Try gunbroker.com or perhaps Numrich gun parts.
Yes.
Yes, but, it will take a gunsmith to do it right.
Yes
Your J.C.Higgins is a sears name that was made by Savage.It is the model 6,or 87.I would use these madel numbers to cross reference the correct scope base and rings for your firearm.I would look at the old redfield mounnts as they made these for a lot of older model firearms.Good luck in your search.