I would like to see an in-game way to post items you would like to buy, to include UVs. There could be a 10% listing fee, as a crown sink, with 5% refunded if no one sells you the requested item before the time expires. Refunding only part or even none of the fee would help prevent people from using this feature to drive up prices. This would make looking for that one special item a lot easier, especially those odder ones. It would also let people who want to craft just to sell things see what is going to return their investment quickest. If this can't be done, maybe allow vendors to pay more for UV items?
The bazaar would work in theory, but something like the Auction House would avoid the language barrier of each forum and the search function that doesn't seem to find things even when you type them exactly as in the post.
Another idea would be to let you search for UVs in the AH. I'm sure this has been suggested before, but I'll repeat it just for good measure.
No for a separate area. Do not need.
As for a 'UV search bar', ok, I guess. Although you could probably 'Sort by UV' and mouseover all the options; there shouldn't be that many.