I have an external website where my products from Odoo are shown with a nice design, search engine, and additional functionality which Odoo shop doesn't offer. After selecting a product on this external site, I now need to send the user to my Odoo shopping cart with this product already added.

My question is if Odoo API can create a cart, add products to this cart and then open up the cart web site for the users? Alternatively instead of the cart, a wishlist could be created and filled with products, could that work?

In case this isn't possible I thought of inserting a iframe on the shop page and communicate them using window.postMessage(). So I just could simulate pressing the "Add to cart" button and afterwards send users to their filled cart. What do you think about that solution?