In "Inside Llewyn Davis" was Mike (Llewyn's deceased musical partner) the Gorfeins' son?
I am most interested in in-universe proof, but would also appreciate quotes of any relevant discussion by the filmmakers.
No, there is no definitive proof given that affirms that Mikey is a Gorfein.
There are plenty of moments in the movie where it would be easy to confirm that he is in fact their son, but such opportunities are never taken. For example:
While this is all circumstantial and based on what characters could have said or done, it's more compelling evidence than we're given to believe that Mike is a Gorfein.