NSFW, NSFK New Senior Manager of Engineering: need some help

So I recently (3 months) got promoted to being a senior manager at my job. At our place we go from dev/team lead to senior manager. There's no manager position.

When I was a dev lead, I was managing one team. Now I'm "managing" 6 teams. I'm struggling or at least I feel like I'm struggling because there's no good, simple feedback. Here are some questions and some things I'm struggling with, hoping I can learn from others and hoping others can learn from this thread:

1. How to handle a boss (VP) (sorry for the non-inclusive language) who is always a sour puss. She's always cranky and accomplishments are never enough for her. She barges into meetings and starts asking random questions, throwing the whole meeting off. Several people have left because of her but…her picture is on the company's website so she's probably not going to leave or change. Her style of managing is very micro managerial and she really demotivates a lot of people
2. VP expects me to know what every team is doing at all times. I think this is a reasonable expectation but I always struggle figuring out CONTEXT behind what every team is working on. Is there a framework someone uses to always be on top of what work each team is doing?
3. VP keeps asking me if teams are staying busy and have enough to work on? How do I track down to a developer level to make sure people have enough work?
4. How do I identify priority for engineering efforts? should I use elastic search or just optimize db queries? that kind of a thing.

I would say 2 and 3 are my biggest struggles and I always feel like myself (and others) never know enough of what is going on with teams. I hate this feeling so how do I fix it? Any help is appreciated. Thanks.