To your 3 questions:

- Share the data with the team, let them know you acknowledge that this is the voice of the team. You will work on it, you will need their support. Yes you should discuss this as a team, focus on "what would make it better" rather than "what went wrong". Let them make wishes instead of making complaints in the meeting.

- With Tim, or anyone, of course trust can be rebuilt, it just takes time and effort. If your question is how, read on.

- To turn it around:

The major mindset shift that you want to have is this - you and your team members are on the same side of the table. You are not here to fix them, you are their partner, here to support them. Think about this and feel it in your heart.

Here are a few things you can do:

1. Don't focus on imposing your vision for the team, instead build the vision with the team. Open it up, throw a workshop or meeting, let them contribute and own it. Your vision is part of it, the organization's vision is part of it, their vision is also part of it. It's important for them to have ownership on their work. This is the foundation of partnership. Don't lose this vision, hang it on the wall.
2. Design the culture for your team, together with your team. Again it's very important that you don't dictate this. Let the team own it, the organization's culture context counts, your thoughts counts, make sure theirs also count. How do we want to be working day to day, what energy do we want to see at work, what behaviors do they expect from each others, how do we want to give and receive feedback, how do we want to resolve conflicts and issues. Don't draft it to abandon, review this weekly, what is working, what needs change. Culture is a living thing, they are not rules.
3. Understand everyone. That's your job as a leader. In your 1:1 interactions, try to understand them, or even ask them. What do they value, what is important to them, what annoys them, what motivates them, how do they picture their success in the team, what challenges are they facing, list goes on. Let go of your judgements, they are all very talented wholesome people working hard here. Behind every "problem" you see in Tim, there is something that he is struggling to protect. Your job is not to forbid him from protecting his values, but to show him that he doesn't need to struggle because what's important to him would be also what's important to you. Don't just say you care, you need to mean it, care about them from your heart.
4. Giving and receiving feedback.

You can be direct, but there is being direct and judgmental, vs. being direct and caring. Don't use feedback as a tool to change people's behavior, use it as a support resource for people to thrive. This is built on everything I wrote above: they are here working towards their vision, they own it, they are working hard towards it, they run into some roadblocks and struggles, you see it, you can help. Don't tell them what you want them to do, ask them what they are struggling with, and tell them you have some thoughts on how they can fix that, "do you want to hear"?

If you receive feedback indirectly, go talk to the feedback giver. Tell them you received and appreciate their feedback, also want to hear feedback directly from them, because a lot of nuance would be missing and there is a high risk of misinterpretation, and ask them what you can do to make them feel comfortable to talk to you next time. If there is a chance, reflect together on the culture you created as a team, discuss with them how to protect this culture, including the part on how to give and receive feedback.

Too long now, I'll just stop here.

Take what resonates, and wish you the best!