Do all Open Access journals charge Article Processing Charges (APC)?

No.

Many OA journals do not charge Article Processing Charges (APC). In fact, 74% of the journals listed in the Directory of Open Access Journals, DOAJ , do not charge APCs.

Publishing is not free. Gold OA journals that don't charge APCs rely on funding from universities, academies, funding agencies, libraries, etc, to function. These are subsidised OA journals and constitute the Platinum OA model in which articles are free to publish and free to read.