I guess so. I once sold a domain a few months old via Sedo and pushed the name within Directi. It's best to inform the buyer and Sedo as well. The buyer must then accept a push rather than a transfer to their prefered registrar. That's it.
Yes, you can. Ownership change will be done through the regular registrar process. Sedo will instruct you.
Unless the domain is with a registrar that does not allow free pushes, I almost always recommend the seller to transfer ownership of a domain at its existing registrar and not allow an unknown buyer to initiate a transfer to their registrar. There is potential for abuse if you're dealing with a dishonest buyer. If you approve a registrar transfer in lieu of ownership push, you have no guarantee that the buyer will receive the domain.