Wishlist and Login are not working correctly. The problem with the wishlist is that when products are added and then you delete them from the wishlist, so that it’s empty and you open it again, the previously added products are there again. https://i.gyazo.com/ddaf3f2f8e392a7a4e8edb92e0a59793.mp4
The problem with the login is that when you move from page to page you are logged out.
I have visited your website and watched the video you attached. Please deactivate all the third party plugins activate the Parent theme.
Clear the cache and check back this will surely fix both the issue.
If the problem continues then remain the third party plugins as disable and provide with admin panel login details to check it myself and help you out accordingly.