Product customisation on a separate page outside the theme

[polguixe]

I want to create a store that will have standard products and customizable products. 

We'll use a Shopify theme for standard products and a custom web app -React-based- for custom products. We have the following questions: 

1. We still want to use the cart in the Shopify theme for the custom products. Flow: User selects a custom product on the Shopify theme -> goes to the custom web app -> finishes the product customization and saves to the cart -> product gets saved on the cart and goes back to the Shopify theme. 
   1. Which API should we use to achieve the above?
   2. Can the Ajax API be used outside the Shopify theme?
2. Where the product customizations options be saved?
   1. The obvious place is in the items custom attributes. Is there a better place?
   2. In the case of complex options like images, where would you store those? Will you upload them to an image server and store the url in item's custom attributes?