I searched this on the net but I didn't find something like this.
For example if one user orders x product. it would be nice that he gets an email with the confirmation, and below the order details something like
You might be interested in:
Then, show the related products/upsells/cross sells.
Is this even possible?
I do know HTML, but I don't know PHP in detail.
I am interested in full code to write this transactional email, do not worry for design details, but for the functional details.
Yes, it is possible. However, without PHP knowledge, you'll hardly be able to implement it. This thread shows the example code on how to implement related products information in the checkout page, which should be easily adaptable to be used in the mailer instead. Unfortunatly, I do not have Magento installed, so I cannot help you any further. Good Luck!