Yes.
Not recommended for full choke
50-100 or so
You need to have it examined by a gunsmith. The answer could be yes, or it could be no. Depends on how it is choked.
Yes your Winchester model 1897 pump action shotgun can shoot buck shot through it.
Not recommended
The JC Higgins Model 20 is a well-made firearm. Provided you have it checked by a competent gunsmith, it can handle any standard 12ga 2 3/4" shotshell. If the gun is not choked 'FULL' you should be able to use slugs.
Yes it is a direct fit.
Slugs and shot are simply the contents of the packaged shotshells. Any shotshell can be filled with shot of various sizes, including 00 buck or with slugs and any shotgun (single shot; pump, double or automatic) that will chamber that shell can shoot those loadings. One caution is that slugs and buckshot should not be used in shotguns fitted with full chokes. Modified chokes and improved cylinders are probably OK, and full chokes can be used with birdshot (smaller pellets).
If you do not know this or are unable to Google it or Youtube it and find out then I must question your competence in actually possessing a loaded gun.
Start with a fuel pump pressure test.
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You pump fake in a game when you have the ball. To pump fake just tap the 'shoot' button.