1) We are going to migrate to a different server. Our customers take their wishlist very seriously, so I don’t want them to lose their products. Do you know if the wishlist will migrate too?
2) I’m having some trouble with the wishlist too. When I’m logged in and I click on the heart icon in the top bar, the wishlist works. But when I’m not logged in and I click on the heart icon, it says the my wishlist is empty, although it’s not. Could you help me with this? Could this have something to do with our cache?
All the products in the Wishlist remain till the cookies are updated, which means the products would not be there forever.
If you transfer your site correctly, all data would remain.
As for the second problem, deactivate all the plugins except these ones:
Contact Form 7
Mailchimp for WordPress
WPBakery Page Builder
XTEMOS Post Types plugin
If the problem has gone, activate the plugins one by one, checking the issue to detect which one causes the problem.
In case, the problem remains, even after all the plugins are deactivated, provide your site admin access (insert the site credentials into the Private content block under the message area) and confirm the permission for plugins deactivation, switching to the parent or default theme. This testing may take up to 15 minutes. You would better make the full backup of your site.