How does one determine a firearm is a C and R if purchasing from an auction or some other venue.
It either needs to be on the list or 50+ years old. If it isn't on the list and there is any question as to its age, obtaining documentation either online or by phone/fax/etc from the manufacturer may help.
Does one need to bring a sheet of paper with serial numbers that prove the gun is 50 years old, or convince the auctioner?
Like mentioned earlier, what is needed to "prove" it all depends upon the seller. They are under no obligation to accept a C&R, even if you can prove to your satisfaction that the firearm qualifies.
From my experience, if they aren't already well versed in C&R FFLs, no information you bring is going to convince them, whether it is the C&R list, a letter from the manufacturer stating the date of manufacturer, or whatever. I suppose there are always exceptions, but...
If they are somewhat familiar with C&Rs, some sort of documentation on the firearm's age, or a copy of the C&R list, if it is on there, _may_ help. No guarantee though, since anyone could falsify documents they are supplying themselves.
If the seller is very familiar with C&Rs and the firearms they're selling, nothing but a copy of your C&R FFL would be needed. If they know C&Rs but aren't that familiar with the firearm, a copy of the list or some info regarding age may be needed to verify that the firearm qualifies. What is considered acceptable proof is again subject to the whims of the seller, though.
tl;dr version: If you insist on only purchasing via your C&R, verify that it is kosher with the seller/auctioneer beforehand.