Hello @HendrikStelwagen,
Hope you are doing well.
Please, take a look at our MIFARE DESFire and MIFARE SAM portfolio for more details on our featured product for these families. Some MIFARE DESFire are Not Recommended for New Designs; however, you can find the relevant documentation in the corresponding product page. Also, our software and tools should be "backward compatible" with previous versions of these products.
As you mention, some of the information about these products is secured under NDA (Non-Disclosure Agreement), and therefor this information is not public. Please consult the Non-Disclosure Agreement FAQs. You can try requesting an NDA directly from the NDA online form; after your request is processed, you should be contacted by the NXP NDA team.
Once you have a valid NDA with NXP you would need to request access to the documentation through Secure Access Rights.

For this, you could follow the instructions from this page: Secure Access Rights | NXP Semiconductors. Also, I would recommend checking the Secure Access Rights FAQs | NXP Semiconductors.
If you are interested in the IC's, testing or having the cards, I will recommend you contacting one of our Distributors from the Distributor Network | NXP Semiconductors, so you can check availability.
Regards,
Eduardo.