How can we make the button appear after the “in the cart” button?

Hello Anja,

1. The button position depends on how your theme handles the WooCommerce hooks. Please try to switch your theme temporarily to Storefront for example.  Probably it will work. Anyway, the pro version allows to use any custom position you want

2. Yes, the lists are separate. On the admin users page, there will be a new column counting how many items each user have added to their wish lists. If you access the user’s profile page you’ll see exactly the items they have added. On the admin products page, there will be a new column counting how many times each product have been added. Would it be ok for you?