Yet another inheritied M1 Carbine

[INLAND44]

Yep, Type I band. This band has a removable swivel which you can probably find along with the screw. Here's a pic of a reproduction one showing how it goes together.

Inland parts including recoil plates are marked with various initials for the subcontractor and Inland. A recoil plate may be marked 'DI' on the inside face, for example, and you usually have to look close for it. Butt plates for Inland mostly are not marked, so you have to go by the pattern of it - there is a web page for comparing all plates and it may be linked on this site. Your bolt for example may be marked 'OI' on the large locking lug. You can also download many of the G.I. manuals for the carbine showing how to do most anything to it. Don't force anything - it will come apart and go back together easily if you know how.
A correct sling for this will be costly, and there's a trick to getting the sling and oiler in the rear slot, but you can look into that after you get your band parts, oiler and sling.
The gas piston under the barrel should be free to move by gravity after the slide is removed or drawn back. Try to avoid unscrewing the nut that retains the piston. If it's 'frozen', firing will usually release it. If the gun doesn't cycle when fired, we can get into what you have to do later.
The carbine should be detail stripped, cleaned, inspected and lubricated before firing anyway.