You can do an exact search using double quotes (" "). That can really help reduce the number of responses. The advanced options, like using the minus symbol, hashtags and such, could be pretty cool...but not all users will understand that. But we'll continue to investigate what is available in the search engine configuration.
That sounds very good and do-able.
As for the initial idea, I think we could possibly save the filter criteria so you can come back and forth. We do this in the Knowledge Base presently.
In the Proposal page, we did add a mass approval button at the bottom of the page. We think there's a better placement for the button, but we wanted to get something out there for usage/feedback.
So if you filter on tasks by status or user, you can 'Mark all as complete' which will move the filtered tasks to the next status (pending approval or approved, depending upon the User's role).