Thinking of the top of my head here.
You could implement a custom form (using HTML and some back-end language like JAVA, .NET etc) and with the help of the Airtable API you can store the form data into your Airtable base.
Since this will be a custom form you could add a link onto your form which will point to the “terms and conditions” document you want your users to download before submitting the form…
If you enter a valid URL in the 'Add some help text' area for any field in the form, it will be converted to a clickable link — it even opens in another tab! (Of course, you’ll have to have your T&C hosted somewhere; presumably, a shared link on a virtual drive — Google Drive, DropBox, and the like — would suffice.)
Here’s how it looks using a checkbox field and Airtable’s own Terms of Service as the target.

(Note the space between the URL and the closing period!)
That is to send info with the form, not no compose it.