Hi,
You can create custom fields of the table "order" via the menu Display>Custom fields. These can be displayed during the checkout.
You can use one of the type "checkbox" for the checkbox and you can potentially use one for extra text with the "custom text" type.
Also, with the title of the value of the checkbox, you can use a translation key and then translate it in each language and in the translation, you can also use HTML in order to have the link to the PDF or joomla article.
The information of the checkbox checked or not will be stored in the order when the order is created and you'll get the order creation date/time and the order user IP address as proof.
Note that you can have the checkboxes required or not with the custom field "required" setting.
However, if you have one custom field for each checkbox, the required will apply to each one individually.
If you want to have the required to apply to two checkboxes at once so that the requirement is "at least one must be checked", then you have to have the two checkboxes in the same custom field.