Thank you a lot for the answers!
By "integrate" in the simplest form I mean: to output a field with product options/sizes etc. and an add to cart button that a user can copy-paste under the products on the existing website. The order button adds everything up to a small pop-up field cart and then the check out can be on a separate page or a pop-up field.
I think I thirty bees has a module that makes a block of the shopping cart, the others "order online" and the product attributes can be solved similarly.
The website is www.sevoa.com .
How Abantecart achieves that is by having an html code generator. Basically they output a product only page like that: https://sevoa.com/abante/index.php?rt=r/product/product&product_id=123 and this gets outputted in a pop-up on the page when "order online" is clicked.
This is the button code: "Поръчай онлайн."
Lesley, I have literally tried 90% of all supposedly ok ecommerce solutions out there - trust me it is really a mess.
If there is a way that we can do module to output that "product only page" the "order button" and the "cart" it would be possible I think, or I am wrong? I am truly eager to start using thirty bees only and I am ok paying for all that and then sharing the module publicly for free.