Any of your domains that are listed at Sedo can be sent to auction when you receive an offer. However if there are no additional bids, you are obligated to sell at the offer price.
Keep in mind, if you make a counter-offer instead, the option to send the domain to auction is off the table.
As for your second question, that is sometimes a headscratcher for me.
I have submitted names in the past for their various auctions including their Great Domains auctions, many of which get rejected. Then I see (what I consider) inferior domains run in those same auctions...