I’d set up a Keyholder group that requires people to request membership. Then create a category that’s visible to everyone, but only Keyholders can reply to topics. Then create a topic with the room calendar in the first post. That way everyone can see the calendar, but only Keyholders can add events to it. This isn’t ideal because you have an entire category dedicated to controlling access to one topic. 
I’m not sure this is possible with the Calendar plugin. It doesn’t really track overlapping events so the only thing stopping people from booking equipement outside the proper time is relying on people manually checking the calendar. Also, are the people booking equipment in the Keyholder role? If not, it might make blocking them from replying a problem.
Given that you need another calendar with another role, I’m wondering if you might be better off relying on the honor system than trying to set up a system to enforce the rules. So you’d have an open category for all the calendars and a topic for each specific calendar. Maybe assign people to groups so that people can keep track of who’s who and use social pressure to prevent people who aren’t authorized from booking rooms and equipment. But not try to restrict people using software.
See also:
I’d try that and if you can’t get it to work, maybe see if you could get help from marketplace.