I know there's a new shop system and that's great. However my concern is I can't interact with a shop I had no sales in, for example my food gallery. I was using it to keep my foods to feed my gourmand pet in a better order. However I can't interact with ot at all to empty and set up a new one...

I'm not really sure what your problem might be. Have you looked at the linked thread on the News Page about the new shopss?

I know that when the new shops came out there weren't any features in my old shop to facilitate movement until I had created a new shop. Once a new shop existed for me the movement features popped up, including the "all" button which didn't exist at each item and the "move to" drop down at the bottom of each page.

If you don't see these things even though you have a new shop, your browser is probably in some way incompatible with how Subeta works. Try disabling extensions/add-ons or changing browsers and see if that helps.