Different Product_Code

Yes. If you create a characteristic and add that characteristic to your product, you will get several variants of your product and each one will have its own code (sku). Then, when the user select the characteristic and add the product to the cart, the corresponding variant is added and the user will be able to see the product code in the invoice.

Could you give an example of product information in your CSV ?

Your CSV is not correct.
On the first one, you have that:
10000001,,10000001.jpg
But the three first columns are:
product_code,images,product_parent_id
The image should be in the second column, not the third.

I see that you didn't specify any product code on your other lines so HikaShop will generate it automatically.
Also, I see that in your product_parent_id column for your variants you didn't specify the product_code of the parent but something like that: 10000001_variant_X

If I'm following you, the product code of the first variant should be 1000000022Regular, so the first variant line in your CSV should start with this:
1000000022Regular,,10000001
First, the code of the variant, then the images if any, and then the code of the main product.