The bidders are not 'private', it is a private listing. Hmmm, not sure what you mean by the listing having disappeared. Did you have a bid on the item? Then it will appear in your Did not win file. Did you have it in your Watch List? Then it should still be there, at the bottom because it has ended.
So, . . . 1) ebay cannot be sure these 'private' auctions, or any other auction, has real bidders and not shill bidders. Unless the shiller is dumb enough to use another ID in her own name and address, - not likely. If she uses that of a relative across the country or in another country, ebay will never figure it out, not in a billion years. Which is why many real bidders won't even consider a 'private' auction. The following link explains about this type of listing:
http://pages.ebay.ca/help/sell/private.html
Ebay does not encourage this type of auction, except for 'adult' things and the like. Sellers are foolish to use them because there are so few bidders as it is, to discourage the honest ones is self-defeating.
That said, it may be a perfectly honest auction. I have bought things that way and the auction was fine, sometimes where I was the only bidder, - doubtless because others saw the 'private' and moved on.
2) You can know the price if you had the item in your Watch List (or of course, had placed a bid). Do you know the item number? You can enter it in the Search bar. Do you know the seller ID? Then beside the Search bar, click the word Advanced. Over on the left where it says By seller, click that and enter the ID, - you can get the completed listings that way.
And if you have exhausted all these possibilities and there is no trace of the auction anywhere, then it may have been pulled by ebay. For VERO violations, for shilling, who knows.
Ultimately, if you are not comfortable with an auction, don't bid. You can report the listing, and maybe enough reports got your listing here removed -- what for, hard to say. Like all things in life, the best protection you will get is that you give yourself, and that means don't bid, or only bid what you are content to pay and do not be shilled up, - ever.
