Iusses with variable product and availability updates

Dear All,I’am trying to complete an online shop. The import of the products is through xml, through a tool that the owner has shown me working on other sites. In my shop I have the problem that WC does not recognize the variable products, or rather it asks to choose the option but there is no option to choose although they are loaded in your panel and the product can’t be added to the cart. Likewise, despite I asked to do not show unavailable items, the store does show them anyway. Furthermore, the tool provides for the deleting of unavailable products. I tried everywhere if there could be an error, I tried to disable all plugins and activate Storefront but nothing, remains the problem. I have put the link as an example, consider that the site has been put into maintenance for the reasons mentioned above but if you need to check it will be enough to write me a line and I will open for your verification.
I look forward to suggestions, ideas and maybe some solutions if it happens to others too.
Thanks in advance for your cooperation. Andrea

The page I need help with: [log in to see the link]