1. Is it possible to stop FARR closing when a result is double-clicked?
add " /stayopen" to the end of the launch result to tell FARR to stay open after launching.
2. Can I get information from the found item into the EditBox?
there may be something i can do to improve the case of dragging and dropping into edit box or chooding jump to directory for these cases, but regardless, i think what you are wanting to, if i understand it which i might not, is to populate your results like this:
choice 1 | restartsearch tz pacific/auckland
choice 2 | restartsearch tz usa
etc
the restartsearch launch command will put the text that follows into the edit box when the item is selected, so it lets you build things like menus in FARR results.