You can try setownership. I know that works to fix things that say "Steal" (before you pick them up). I've never tried it to make safe storage.
Probably not. You can remove ownership for individual items but containers contain lists of item that will probably still not be player owned, havn't tried it though. It won't stop them respawning either iirc.
FYI - the online reference for engine commands: http://www.creationkit.com/index.php?title=Category:Console_Commands
Just "setownership" will make it owned by the player. But safe storage has nothing to do with ownership, and if it's a respawning container the contents will be destroyed when the cell refreshes no matter who owns it.
If you just want a safe container to store things in try my Storage Helpers mod. That's why I originally created it. And the item movement feature is so I can move the old one out of the way without needing a console command.
I had never noticed SetZoneRespawns. Very interesting.