Your Products table is schizophrenic, its entity is sometimes Product and sometimes Variant. This leads to very cumbersome behavior. For example, you'd like the question "how many different products do we have?" be answered by select count(*) from products, but here this gives the wrong answer, to get the correct answer you have to know the Magic Number 0 and query select count (*) from products where master=0. "List all products and how many variants we have for each" is another query that should be straightforward but now isn't. There are other anomalies, like the fact that the first line in products_descriptions is a shirt that has a price and a picture but no size (size is stored in the variants, but they have prices and pictures of their own).
Your problem sounds like you have products in two contexts: (1) something that can be displayed as an item in your store, and (2) something that can be ordered by your customer. (1) probably has a name like "Halloween T-Shirt" or so, and it probably has an image that the customer sees. (2) is what the customer orders, so it has a (1), but also a variant specification like "small" or maybe a color "red". It probably has a price, too, and an order_id so your shop can know what specific item to ship.
You should give each context an entity. Here's how i'd do it
displayable_product
id name
1 "Baseball Cap"
2 "T-Shirt"
orderable_product
id d_product_id order_id size color price
1 1 123 red 9.99
2 2 456 small 19.99
3 2 789 medium 21.99
displayable_content
id d_product_id locale name image
1 1 en_US "Baseball Cap" baseballcap.jpg
2 1 es_US "Gorra de Beisbol" baseballcap.jpg
3 2 en_US "Nice T-Shirt" nicetshirt.jpg
4 2 es_US "Camiseta" nicetshirt.jpg
You should probably use locale instead of country in the display tables to account for countries with more than one language (USA, Switzerland, and others), and you might separate the size and color into its own variants table. And if you need country-dependent data on the orderables (like different prices/currencies for shipping to different countries), you'd have to extract a country-dependent orderable_content table, too.