Yes, it is for free.

No, that has never been permitted. You can request a specific flag to be flown at the state Capitol but that is very limited. Only flags of the: United States of America; a state of the U.S.A. or a political subdivision; the District of Columbia; Puerto Rico; the U.S. Virgin Islands; any territory or insular possession subject to the jurisdiction of the U.S.A.; an Indian tribe recognized by the U.S.A.; any foreign jurisdiction with which the U.S.A. maintains diplomatic relations or its political subdivisions, to include the United Nations; flags of recognized military organizations of the U.S.A. to include the VFW, American Legion, and POW/MIA flags.

Non-flash photography is permitted for everything except the Amistad collection. The lighting in the building is great, and you really won't need a flash.