For 1, 2 and 3 we don’t have plans to include this functionality into standard REST API in the nearest feature. We’ll add a userId information to the /userInfo controller - then you’ll be able to update the current user by the entities REST controller or by some custom service.
As for item 4, we’ll think about it. Probably, we’ll add full text search functionality to the REST API, but I can’t say when this will be done.