First creatures are exchanged, then artifacts are exchanged. It's possible that the same artifact creature may be involved in both exchanges.

No permanents are targeted by this effect, so permanents with Shroud may be exchanged this way.

If one of the players doesn't control a creature at the time the exchange would be made, that part of the effect does nothing, but the exchange of artifacts will still happen. Similarly, if one of the players doesn't control an artifact at the time the exchange would be made, that part of the effect does nothing.