1. No, because the placement does specify "your" and the ability after the colon on a placed card is not active while the host does not match the specifications. The reason it will work on a Converted Herod your opponent controls (or even owns!) is because it just specifies "a Herod."
2. The bearer is Protected from convert so it's moot, but if that weren't the case the answer would be the same as above.
Now, don't try to extrapolate this to the placing characters because it's different. The placer and the placed card are two different cards, so the rule about the text following the colon not working if the specifics on who it's placed on change. The placer Heroes' have three different abilities; search, place, and a delayed trigger contingent upon a condition unrelated to the placed Enhancement.
