How can I get rid of the /panel redirect and the e-mail as username? I'd like to operate a site without any user accounts, is this possible?
Users don't have to create an account in order to make a purchase. But without the option of user accounts, they won't be able to log in to see their invoices, downloads, and transaction history.
Shopkit forces email-based login to make things easier for the customers (they won't have to remember a username). But if you really want to remove the frontend form and login via
/panel instead, take a look at the routes.
Since I am developing a single page store, I'd like to integrate the cart in a popup overlay. I'd also like to integrate all the following steps of the checkout in that overlay. Is this possible somehow?
As a starting point, you'd have to override Shopkit's default
templates/cart.php with some custom form actions. Then it depends on which gateway you're integrating with – PayPal will have a different process than Stripe.