In this business we usually refer to the stores themselves, such as Penny's, as the 'client' and the outfits that are putting together the shops for the clients as the 'companies'. So yes, to shop a particular client you need to sign up with the company that is shopping for them.
As for the merchandising question. Every merchandiser starts at some point as inexperienced. My understanding is that the companies prefer experienced merchandisers, but if they need someone in your area your 'dm' or district manager, will work with you to get you started. Merchandisers seem to love or hate particular companies based on their 'dm' and seem to most frequently stop working for a particular company when there is a change in their 'dm'. Employment situations for merchandising seem to be more diverse than for mystery shopping. In some cases you actually are a part time employee, while in most you are an independent contractor. In some cases you are paid hourly door-to-door while in some cases it is flat fee for the job. Certainly an advantage of merchandising is that you have a regular schedule of when you are servicing various locations so the work is far more steady than mystery shopping, which is a visit-by-visit contract situation.