Question 1: Why would anyone maintain the dust tree in this case? The only incentive I can see is to earn mining fees from dust. But if it is truly dust (like the 11% of blockchain data containing $0.02 USD of value), then there are no fees to earn.
For the same reason people seed torrents: because they want to, and/or it's no big deal to them.
Question 2: If dust is "dusted off and used", does this require the other nodes to download the dust's entire history again? Or alternatively to trust the nodes that validated the dust?
No - by spending the dust, the dust makes it into blocks. Any transaction that's very recent, dust or otherwise, will make it into the main transaction set just for being recent.
Question 3: Blocks can be mined which contain no dust. If most miners restrict themselves to this type of block, isn't it best for other miners to do so also? (since a dust block would appear to take a long time to validate and thus risk creating an orphan. Also even if all the miners deal in dust, won't dust blocks take much longer to propagate through the network, leading to the same effect?)
Dust transactions often arrive with transaction fees, and miners aren't going to go out of their way to make sure they're not helping the network. The dustbin isn't that huge - the miners don't benefit in any useful way from having 99% instead of 98% of their disk free. I anticipate miners recognizing they need the whole data set if they want to mine, even if the extra fees weren't an incentive.
It seems to me that this is a sneaky way of introducing dust demurrage via economic incentives. i.e. if you make it cheap to sort dust records from valuable records, and no party profits from maintaining dust records, then we end up only maintaining valuable records. Just like if we changed the protocol rules.
If everyone stopped seeding data because there was no economic incentive to do so, The Pirate Bay should have collapsed by now due to lack of seeders.
