It seems that Euros' psychosis is a manifestation of her loneliness and inability to comprehend human emotions. She recalls that in her childhood, she loved to make Sherlock laugh but in reality he was screaming. Contrast this with her drawing pictures of Sherlock's gravestone and killing his best friend because she wanted someone to play with her.

Every aspect of her character is a duality. She clearly feels attached to Sherlock, but at the same time has to get the guards to restrain her from seriously injuring him. We can see all of this culminating in her recurring feeling that she's all alone on a plane that is crashing and no one is there to help her - this is probably a perfect metaphor for how she feels her life is, especially in Sherrinford. It's ironic that even with her supernatural intellect, she falls victim to human emotions of belonging, and responds almost tearfully to a hug from Sherlock letting her know that he's there for her.

We're also never told details about what the relationship between Eurus and Moriarty was. It didn't seem like Eurus manipulated Moriarty at all - he just seemed content knowing that Sherlock was going to be mentally tortured by Eurus and would mostly likely kill Mycroft. Moreover, Moriarty seemed to already know about Redbeard almost as if he had discussed it more with Eurus earlier. Maybe it was just a metaphorical representation of what their actual conversation was - Eurus must have showed him that she can use Sherlock's overridden memory of Redbeard to cause the Holmes brothers incredible pain, so the word Redbeard was just symbolic in that conversation.

I came across more analysis here: https://goo.gl/aFjhHE. It has a bunch of enthusiasts curating all the best theories, episode discussions, etc. about Sherlock in one place.