Re: Embeding product onto a 3rd party site
Short answer: no, you can not do that.
Long answer: nothing is impossible, yes you can do that. You will have to check how ZC add product to cart, you will also see how it uses session id to store the cart content, and see if you can somehow do that, please note that sessions can not be shared across domains (for a very good reason)
I no longer provide installation support on forum for all my modules. However, if there are real bugs with the modules please feel free to contact me