1] Can you add more custom products than the ones already set by the developer?
2] In Demo, when you add a product and then continue shopping for more products, there isn't a simple way to get into basket, in fact, no basket icon is available on the website, why is that?
3] Cards, they cannot be fully edited, on the Demo, they come as Christmas Cards, only the recipient can be changed, a customer might want a Birthday Card instead, so what is the solution?
4] Can we not allow customer to either select cards from our store and/or allow them to upload their own designs?
1) Yes, of course - that is the main point of the plugin
2) Because the demos are not setup to use the WooCommerce cart system to it's full extend. Usually it works as any other WooCommerce page, with cart icons in the menu bar (depending on your theme, other plugins)
3) Create a birthday cart product, you can also allow to switch between different types in the same designer via the change product feature
4) If you use the change product feature you could also provide a few templates that allow image upload/ full self design, yes.