SELECT json_field FROM data WHERE json_field->'age' > 15
Part of the performance increase for hstore is improvements for GIN indexes, and according to the author can be applied to json. So yes you can use indexes on your hstore or json documents.
Yes, for a project I'm working on, I had a JSON array of objects that each had a key called name.
I have fast indexed queries that return any rows that have an object with a given name in it, and for full text search on that name along with a few other things.
I.e. can I do something like SELECT json_field FROM data WHERE json_field.age > 15 ?