To search for product listings by anonymous sellers, leave the field "Seller username" blank. Do not put in the word "anonymous" as it would search for product listings by a user who registered and made "anonymous" their username.
You can sort by how many offers each listing has received to see what is popular, but for privacy reasons, we are not disclosing how many offers other users' listings have received. Since you do not see if a listing even has offers, then it is possible that a seller have may have had no offers on any of their listings.
This search is also for if you want to search for a seller's invite-only listings. You will need the password to view the listings, though.