Have you ever been to community theatre where theatrical performances are made up and performed by the community?
No, I have never heard of that. Are the performances good? 
I would imagine that would have a lot to do with the community! lol Many community groups are non-profit business with large memberships and even have a work staff.
Oh wow! Where would I find out if they do this in my area?
I would look online for resources. Many theatres are small groups that perform in borrowed spaces and others are large groups that have permanent facilities.
I never knew that, I always thought of Broadway shows. How do they get money for props?
I would think they would depend on community assistance and donations. The theatre is used as a social development tool and to promote ideas such as human rights, gender equality, etc.
How would they promote ideas, just in the plays they produce or in advertising in the pamphlet they pass out? 
Most likely the messages are conveyed through performance and may also be shared in promotional pamphlets.
What age do people generally start performing in local theater?