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Yes
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Yes, you could do it that way, re-using Bitcoin's Script system for signatures. I suppose it might be useful to require m-of-n signatures for a domain to be transferred to somebody else. I wouldn't make them full-fledged Transactions, though (multiple "inputs" to a domain renewal or transfer doesn't really make sense, for example).
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Yes, I think that's right, although I was imagining that the DIANNA and bitcoin difficulties would be kept separate and not combined. Combining them is probably a better idea (if you find any blocks that satisfy the bitcoin difficulty but not the DIANNA+bitcoin difficulty you can still announce them on the bitcoin network and get the block reward).
RE: what is the incentive for maintaining the DHT: the registrars/mining pools would, I think, be the primary maintainers of the DHT and their incentive to maintaining it is the registration fees that they charge.
I haven't thought deeply about possible attacks; if a DHT is used then you have to defend against Sybil attacks (you must have some way of checking to make sure the data you get from the DHT is valid, e.g. have the DHT nodes return a Merkle branch down to the data they're returning that you can verify hashes to the correct Merkle root).