Not quite sure I understand, but are you looking for a way to integrate the auction into the Facebook page app?

Multi-site is the built in ability provided by WordPress to set up multiple sites on the same domain either by sub-domains, i.e mysite.website.com, or by folders, i.e website.com/mysite.

You can find more information about that on wordpress.org

a. Using multi-site, yes it’s possible to allow users to set up their own domains and auction items on their own platform. Though you cannot manage their auctions, or control the payment process.

b. You can use a variety of member plugins available to charge them to set up their sub-domain/folder sites (as stated above), NOT to post auctions (please understand the difference).

Hope that helps.

a. the user to post the auction, not just admin as we wd want the content to come from users
b. the site to charge a commission on trades, and/or an upfront fee?

many thanks

Nick