It looks very original to me. Too bad someone took a belt sander/spokeshave to the stock, but at least you can see what was on it originally. I'm sure someone can help you find a 'new' set of wood.
With a good cleaning, the metal will look a lot less brown and a lot more blue/grey as it did originally.
Overall patina looks very original and I think you can be pretty sure those parts, including the magazine have seen long service together.
Your backsight aperture is probably repairable with a bit of careful welding and filing/machining. The matching patina and wear would suggest that rather than replacement with another MkI sight that is likely to be near-new, as most of them seem to be.
A close-up of the SN on the bolt would be useful, but unless your rifle's bolt was replaced with one a few numbers off for some reason, it sounds and looks likely to be the original.
Is the mag a LB-made one?
The thick muzzle band is not one LB made for long I believe. They went to a light, cheaper thin steel that is much easier to remove/refit and does the job just as well.
Not sure what the point of that thick band ever was actually! Trying to add weight at the muzzle end of the rifle perhaps? Savage stuck with it for some reason.