Can't think of any reason why an 1894 would have a loose barrel. That is indicative of a major problem. Wouldn't spend a cent on it until the cause for this problem is determined.
Ditto ....
However, I'm able to hand tighten past those wear marks to a point where the sights are canted too far to one side, compared to the receiver. If I make the barrel level, and reassemble everything, my headspace checks out, but I know that my barrel isnt torqued. Is there a way I can tell if this is a parted out rifle?
How far past? a few degrees - 5, 10? or are we talking like 45? (each flat past would be 45^

) and too far to one side would be to the left ~ clockwise ... right?
If it's only a few degrees clockwise, I would guess bolt stretch (the barrel has been torqued past the ability for the threads to return to their original shape) ~ measure the threads (both receiver & barrel)
As far as I know (and I only know enough to be dangerous) there is no way to (definitively) tell if a barrel on a Winchester is original to the gun - some research on calibre, length, profile etc to determine if that model was ever sold with that barrel configuration might help. Or not - could be a custom config from the factory ... if you are VERY lucky you can look up the serial number to see if records about it's manufacture & delivery details exist . Though probably not worth the cash if you got it off an auction.
To determine if it is a mix master .... does the condition of the action match the bore condition, a "good with strong rifling" 110 year old bore has not see a whole lot of action - I would expect the action to be pretty tight without much wear on the internals or slop.
Your big indicator will be the screw condition .... were the slots sharp and clean? were they too sharp and too clean are they replacements or are they mangled beyond recognition. mangled screws = amateur/hobbyist
If they are damaged in any way .. why? replacing a part? someone was curious? (did you do it

?)
The most common replacement here would be the link - they wear regularly. The only way again to tell would be to compare the internals to see if they are 'period correct' - a replaced lifter might indicate a calibre change ....
Basically - take it to a proper smith & have the barrel installed properly (or be told it can't be) & you might be ok. A complete restoration ... I am with everyone else. WAY more than it is worth. (the barrel installation might actually put it over)