Cart resets when user logins

Yes. That's the normal behavior. Once the session expires, the cart is reseted. Thus, the products are lost. One solution to implement in the future could be to add cookies to the user browser in order to store his cart so that it could still be retrieved.

For the cart, you could try that instead:
CART_EMPTY=" "

It will still be considered as empty by the browser and won't display anything. But HikaShop won't consider it empty and will still put around the divs necessary for the refresh of the cart.

Unless we find another big bug which needs to be corrected immediately, yes

That's already in the todo list. That's in part why we save the cart in the database. Wish lists will just be carts with another type in the cart table...