I'm not OP, obviously, but I've also been pining for some of their suggested improvements to Quick Answer. For me, the biggest QoL improvement would be the ability to ask follow-up questions. I believe it could be nicely integrated as a "ask a follow-up question" bar at the bottom of the Quick Answer section as in this mock-up. 
When asking a follow-up question either of these options would work for me:
- Being redirected to Research Assistant with the included context and and quick answer of the search
- Having the conversation continue in the Quick Answer section of the search page
I frequently find myself first doing a ?-search but then manually having to repeat an !expert search afterwards to follow it up.
As OP also mentions, being able to customize the length/style of Quick Answers would also be nice. This could simply be in the form of a custom system prompt option in the settings menu, similar to the custom Assistant setting. Examples of this could be "The user only wants a single option, and they prefer the laziest possible way to do things", "The user favors products that are made in Mexico." or "Respond in a single sentence".
