No, you can use the dashboard permissions to limit who has access to dashboards, management zones are used to filter what data can show up on those dashboards. So if a user didn't have permission to see the services in a dashboard based on their management zones they would see an empty dashboard.
Not right now no. That would be a change to Dynatrace to do something like allow dashboards themselves to be added to management zones (maybe via the tags we can add to them now) rather than just the data/entities displayed on them.
I don't think I've seen this RFE/Idea before you can post that or whatever approach you think makes sense in the Ideas forum.