I think you are probably fine on the type I band. There are a few marks on the top of the stock, but looking at it, I think it's from not losening the band enough to get it to slide off. Which scarred the stock a little. From the side, there is no shadow on the stock for a type III. So you are good. The front sight pin does have a little depress on it. But I doubt it's been removed. Very well could be how the pin was made, or from the install. The band looks like a legitimate Inland WWII band, which is a good sign.
The rear sight was definetly put on at a Armory. Those stake marks are the ones that armorers put on. Why they felt the need to pound them so deep I don't know.
It's hard telling if the barreled receiver is original to the stock. It's anyone guess, and there is no known way to know. It very well might be, and a few parts were swapped when it went through the rebuild. As parts broke, like the top handguard, and the early bolts had a few problems. But it's anyone's guess. But the fact that so many parts are correct after a rebuild is a good sign. Many times carbines were just torn apart and adjustable sights and bayonet lugs were installed. Sometimes just the adjustable sight, as it appears in the case. Otherwise they were left all original, except for non-serviceable parts. But as I said it's anyone's guess.
My personal opinion, which isn't worth much. I feel it's probably the original Inland receiver group to the stock, with a few parts replaced during rebuild/inpsection. Everything looks pretty consistant in wear and finish. If nothing else it's been that way since rebuild. I would sincerly doubt it's a recent put together rifle. I believe it at least left service that way.
You will never know for sure what is original on it, but you still have a very desireable gun, that many people would give their left hand to own.
Welcome to the club by the way! They are very addictive. If you haven't got a jump holster yet, you should find one. They look great together.
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