Why does Gwen wear her black dress every time she meets with morgana and what did the note say that Gwen gave to morgana in the hollow Queen

I think it is because she always sneaks out at night and wants to go unnoticed.

The black dress represents that Gwen has gone ~bad~, I suppose it being a kids Zeigen they have to simplify somethings. The same thing happened to Lancelot when he came back from the dead and was working with Morgana, he was in all black too.
As for the note, unless they showed it on the Zeigen I don't think there is any way of knowing.