I understand the technical reasons behind this and of course an ADD button doesn't make any sense. That was some kind of reflex to mention add/remove as one feature.
But I would argue that without a REMOVE button, the cart popup loses a lot of its purpose. I'd say the main use case for the cart popup is reviewing one's selection. I think the expected behaviour would be that it's possible to alter that selection in the same place. That would be consistent with the rest of the UI. The user doesn't differentiate between the gallery popup and the cart popup, this is a purely technical difference and not visible to the user.
Actually I can remove items from the cart in the cart itself, why not in the popup? If the popup is open and I remove the current image, it just closes – the same solution could work with a REMOVE button in the popup (although I would strongly prefer your idea of showing the next image).
As for #2 inheriting all settings from the gallery, this is mostly a technical limitation because we can't really use the X3 gallery-popup for opening a custom range of popup images. It could have worked like this, but unfortunately it doesn't.
Is there a way to configure the cart popup seperately? Or at least have it have an ID or different class to target it in CSS? If I see it correctly, at the moment the classes are the same as for the gallery popup.