Can I choose which specific variants the alerts will apply?

Is it possible to apply the alert to specific variants of a product and not to all of its variants? For example, one of my products called Cool Kicks shoes has 5 different sizes as its variants: 6, 7, 8, 9, and 10. Three of these variants (6,7, and 8) ran out of stocks but I do not want customers to see the floating button on all three variants but only on size 7. Is this possible?

No, it is not possible. The app is dependent mainly on the data gathered from the inventory in your Shopify admin. As soon as the inventory of a product or a variant of one of your products goes down to zero, the app would automatically detect it and apply the setting. You can only manipulate this if you manually set the product's inventory to zero in an in-stock product or do the opposite, which is to manually add a number to the inventory of an out-of-stock product to prevent the app from detecting it. But then again, why would you do that, right?