Very nice 99RS.
From here it looks like a pre-war M1907 sling. If gov't issue and as nice as it seems worth a few bucks too.
Go ahead and clean it with a rod. You would be prudent to use a bore guide so as not to rub the rifling unnecessarily at the muzzle. Avoid pushing crud into the action by the simple expedient of wadding up a rag behind the chamber. (Keep the bolt open.)
"You can lead a man to logic, but you cannot make him think." Joe Harz
"Always certain, often right." Keith McCafferty
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