Updating meeting room policies

My library (municipal public library) is working on updating the meeting room policy for a number of reasons. Two major pieces of focus are what types of groups/organizations are able to request use of the meeting rooms. The other piece is requiring all meetings to be open to the public.

Currently the policy indicates that the primary use of meeting rooms are for library-sponsored activities. Any remaining time may be scheduled by nonprofit organizations for educational, cultural, or civic activities on a first-come basis. Use of this room does not constitute endorsement by the Library and must not interfere with or be disruptive to other library users.

Questions #1 - Is there a legal requirement for public libraries to limit to non-profit organizations? If not, what is the basis for limitations?

I am leaning towards shifting the mindset from limiting meeting room use to the above mentioned non-profit organizations (education, civic, cultural, etc.) and to advance public libraries in supporting local businesses and economic development in our communities.

Question #2 - Is it a legal requirement for all meetings to be open to the public?

Question #3 - Is there any benefit for the different type of meeting rooms to have different policies? Why should Large Study Rooms, Conference Rooms, and/or Meeting Rooms policies differ?