You can use a flat bed but typically the containers are put on a chassis, which are also lighter than flat beds for the most part
Yes, flatbeds are used to haul containers, you must use chains and straps, however, you cannot pick up a high cube container with a flatbed, you must use a step deck or a chassis. No, not anyone can pick up a container. Your company must have an SCAC code and be on file/registered with the railroad or port where you are picking up from.