About forwarding email to professors
tl;dr Agree with your advisors on how you communicate

You've certainly not made a "mistake". But what you're realizing is that your assumptions about:


Which language to use?
What information should be shared?
How verbose should you be?
Whose responsibility is it, and who has permission, to update the 3rd person of the triangle about communication between the other two?


and so on. In your place I would talk to both my advisors, separately or together if you ever meet, about your "email routine" - what they expect and what, and what you expect and want. Then none of you will surprise/annoy the others with undersirable email practices.

And this is basically true about most kinds of collaborations in groups of people which don't all communicate together in a common forum.