I've got 4 (working on 5th!), but the one that's specific to this issue is Mission: To Manage. It's on Amazon etc, but (shhh) I can get you a free digital copy - send me a DM if you want.
It's hard to say, not knowing your friend or what she is doing.
I bought a whole case of these books to give to everyone in an office I was advising. The book sparked a lot of beneficial conversations.
https://www.amazon.com/Extreme-Ownership-U-S-Navy-SEALs/dp/1250067057
These are pretty standard questions that companies often survey of their entire population so they can identify problem managers, so you're on the right track. The only generic question I'd consider adding is "what should I continuing doing". I'd also recommend providing a scorecard for 1-to-5 (being clear that five is the highest) and ask your team to provide comments for each score as well. This way you'll get both qualitative and quantitative information from the exercise.
As for more nuanced questions, the most common I've seen lately have to do with the pandemic. Is your team distributed or fully remote? If so, consider adding a few questions like "Do I properly enable our team to be successful while distributed/remote?".
Also, be very clear about how anonymous this survey really is. Is it set-up so you cannot know who provided the answers, or are you just promising not to look on the backend of the system to find out? If it's truly antonymous, consider providing a link to the software you're using explaining how it works and remind them that their comments could still give away their identity. This is a good exercise in trust for your team to learn they can be a bit vulnerable by pointing out criticisms without getting in trouble for for it or being lied to about how the survey works.
If you want to go one step further, Group Dynamics and Team Interventions is a great book is full of surveys you can give your team and the management theories involved that will let you dig into more specific issues. I consider this book to be a bit like a maintenance manual for dysfunctional teams that will help you identify the root cause of any issues.
Someone talked about Crucial Conversations the other day on another post. I think this is another example of when this can be useful.
The principle is essentially that we are naturally poor at having useful conversations when emotions are running high and there is consequence to the outcome. We either dodge the conversation entirely, talk around the issue, or go in too hot and heavy - none of which are actually a productive approach.
Navigating crucial conversations requires candour, a solution-focused approach, and the ability to offer direct comments without making the other person feel threatened. You also need to have a really clear understanding of what you want the outcome to be, and stay absolutely focused on it.
I would try something like the following, in private to mitigate the threat risk:
>Michael, I've noticed you're often quite critical of the staff on my team. Having worked with them for a couple of months now, my experience is that they're passionate and hardworking but lacking in confidence, and I'm worried that our frustrations with them are counterproductive. I'd like to take a more encouraging and coaching-oriented approach to leading this team - it will take some time to move them past these mistakes, but I think this is the most reliable way to do it. Can I check that I have your support with this?
Obviously adapt to the specifics of the situation and what you're trying to achieve.
Dudes tripping, nothing wrong with headphones.
Also these might be a good in-between. I use them for gym mostly because I want my own music but don't want to seem unapproachable: