Dear Brother, You've posted an excellent question. I would think Bhai Gurdas's Vars are referred to as "Adi Granth di kunji" (key to the Sikh scripture) because of the Vars' systematic attempt to explain Sikh tradition up to that point.
I mean "systematic" because the vars often tackle one theme at a time and expand on that theme using metaphors, examples, and other literary devices. They are written in, usually, very simple Punjabi and in a very beautiful rhythm that makes them ... "catchy".
As far as your question about if that notion of "kunji" comes from oral or written text, I thought I knew the answer but it seems harder than I thought to locate the root of that. At first I thought we could attribute it to Bhai Vir Singh's publishing of his Grandfather's (Giani Hazara Singh's) translation of the text. But that translation has no introduction, so unless the term "kunji" shows up elsewhere in that text I'd have to rethink that thesis.
A text from the 1700s called "Sikhan di Bhagatmala" takes Bhai Gurdas's 11th var and elaborates on it. So we have the first commentary on a commentary in the Sikh tradition at that point! It just goes to show you how important Bhai Gurdas's work has been in the Sikh tradition.
The Manuscript questions will take some more research to answer. If you understand Punjabi well, I recommend Rattan Singh Jaggi's work on Bhai Gurdas, as well as Gursharan Kaur Jaggi's work (I'm pretty sure both are published by Punjabi University Press).
Good luck and keep plugging away at these questions!