DAPI allows ANY two peers on the network to communicate directly and send ANY messages they wish between themselves. Therefore all future implementation of this type of technology (payment channels, one click purchasing, etc) is actually done in the lite wallet itself (python, javascript, etc). So it's more like you telling the website "hey my username is Evan",  then it sends a temporary request which allows the communication channel, after which let's say you want to buy socks, the website will ask your wallet directly, "Do you want buy socks from XYZ for $14? (along with the correct payment address to send to, etc)". Then you click OK, which sends the payment to that merchant.

If you broadcast a payment using the first tier, there will be normal fees. We don't need RBF because we can calculate a fee per kb using masternode quorums for the rest of the network. For third tier users, they'll pay for processing time they use on the network, not per transaction. Each time you do anything, the network will update your profile and say "User Evan used 123 milliseconds of processing time" via a quorum action. All users get some amount of free processing time, which will be calculated by the network to allow 90% of our users to maintain 100% free accounts.

In economic terms, our heavy users and economic inflation (e.g. creation of new coins being paid to the second tier) are going to subsidize our regular users by paying for their processing time on the network. I think the target audience should have completely free access to the network and we can shift things around to make that happen.