not all my vita characters are the same level as
my ps3 characters??
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the trophies don't seem to auto-unlock, so as far as we know at the moment, they're separate.
as for syncing, you need to make sure the last device you played on was idling in the main menu for a bit while logged in to PSN and then check the other device. it auto-syncs in the background, but you have no indication of the current sync status.