Is it possible to have the element "text" (which the customer enters) in the order details? The element (and also the element properties) are visible in the email, but I really would like to have this information also in my order details.

Yes, and that is indeed visible and saved - don't really know why they don't also save text input as well. The text is visible in the cart - but not in the order details.

So text is absolute not possible to show in order details (so added to Color, Font and size)

This is really not possible?

We really need to be able to see the entered text and the ID/name of the image selected from the designs, both in the order view screen (saved as meta data so we can include in CSV export). Is this possible?

There is only this option, WooCommerce tab in the settings: