Joanna,
The best place to look for both these answers is in the PMP Handbook:
www.project-management-prepcast.com/pmphb
Page 8 top answers your first question: The experience does not necessarily have to be paid work, but it does need to be in a professional setting.
And in regard to evidence the hours you claim, PMI starts from a position of trust. But, if your application is audited, then your contact persons (you name them on the application) will have to confirm everything in writing.