I would like to allow my customers to validate the receipt of a project by filling in a recipe pv inside Projeqtor.
First of all, is that possible?

No, ProjeQtOr does not manage this.
It is a document, and you can possibly manage the doc with projeqtor, and have validation of the document. But there is notthing exiting to generate this document.
Possibily you can use Delivery or Test Session to generate the doc (using our template report) but I'm not sure it will fit your need.

Secondly, what workflow do you recommend so that it has legal value?

It cannot have legal value inside projeqtor.
You can request your customuer to electronically sign the doc (it provides XML file) and store it with the doc, but I don't know how "legal" this will have face to a jury or a court..

is it possible to exchange with my customers in the form of a chat inside projeqtor?

Yes and No : you can use the activity stream that exist on any item.
I allows some chat-like exchange, sotred as notes, on an item.
But this is always "on a corresponding item" (ticket or activity or action).
It's not a real chat.

Thank you for this very complete answer. I will try and I come tell back for the community.

Fred - ITANéA