To keep it brief I'll limit myself to 3 each.
Absolute Must Gets
- Role Queue (Pretty much a given)
- Hub-Centered Queues (Slightly less important, but could help make Newbie-Friendly Groups for example)
- Community Discussions (It should be possible to arrange and run community nights independent of Faceit's team)
Need To Change
- Balancing (If their 12v12 mode is anything to go by, balancing matches is shocking)
- Their confusing focus on Casual. (Comp is by far and away a more consistent audience, even if numbers are lower)
- In-Game Reporting should be available, possibly implementing some subbing system (Opt-in on queue)
Absolute Must Nots
- Not leaving the community to figure out the system for themselves
- Using bizarre community events (WTF was Clan Wars?)
- Listen to random content creators for legitimate advice.
The last point touches upon the second part of the question. They should be receptive to all feedback, but understand who exactly is making those points. Whilst an Invite/Prem player may have some ideas on how to organise the queue, are they the ultimate authority on how to run a matchmaking system? If there must be some 'council' or 'illuminati' it would make sense for that sort of thing to involve people who have tried this before or at least have notable experience in organising for competitive tf2. Now that comes with a caveat that even those organisers will be biased and have their own views which may be misaligned with the attitudes with the community, but by bringing enough on you should have something reflective of the competitive scene. Again, all feedback should be given weight regardless of whether its a player, professional or organiser but if you want the most robust arguments on how to manage competitive play, its best to hear from those who have been doing it for years.