I'm not at all arguing there's a free lunch here. It's a tough cookie to crack and requires a reimagining of half of computing. I also think it's the only possible way to go.
1) As for the query costs; yes they are there. For public data you could still create pre-computed indexes but for privately shared data the recipients/accessors of that data would need to create appropriate indexes.
In general this scheme indeed requires each producer (person/identity) to also maintain their own indexes.
2) I don't get what you mean by doing a complete lookup.
3) Since this would be a fully federated/decentralized system there would not really be such a thing as server side pruning since the 'server' would just be a peer that indexes public data.
Given that data is immutable clients would simply hold on to the data they need for their calculations and could choose to depend on the server to keep a copy for them.
If nobody (wants to pay to) hold onto a copy of some data anymore then it has been garbage collected.
P.S. Have you looked at the Datomic model? It works quite similar to this proposal with regards to things like storage, peering, computing indexes etc.