I feel like this is a case of Solipsism given form.

Her eye color. :|

Whose? What about it?

Unhelpful comment is unhelpful

"Just because the distinction between us is arbitrary doesn't make it less meaningful", huh? That's a pretty powerful message

I believe the quote you're looking for is "I think, therefor I am."

Aside from what others have said so far, which I agree with, interesting thought that everyone is the center of their universe and that everyone else is just memories.

Information takes time to process by the brain. By the time you really see what you're seeing, time has passed. You only ever see a memory.
Sound takes time to vibrate through the air. The moment of speaking has already passed by the time you hear it.

But something had to cause those memories and vibrations in the air. So even if all she was perceiving was a memory, there's still something corporeal happening.

We perceive dreams and hallucinations, but nothing vibrates or reflects light. How do we know the difference~?

Romeo: I dreamt a dream tonight.
Mercutio: And so did I.
Romeo: Well, what was yours?
Mercutio: That dreamers often lie.
Romeo: In bed asleep while they do dream things true.

I fear that Julia may be finally and irreparably broken...

Not necessarily.

It feels more like the end of Evangelion: she can still choose to be her own self and not just a part of this endless black entity.

The tree, the vines.

If we are the gods of our realms than how do things that supposedly don't exist effect us so?

We are a collection of memories molded by experiences, ripples in a pound. But those ripples have to come from somewhere, something must fall into the pound. These ripples are from other people, each the center of their own universe crying out I am here I exist. Each trying to make sense of the information coming and going, each trying to make their way.

Just because we can perceive dreams and hallucinations; does that mean what we perceive around us is no more real than such phantasms? Does that mean that we should and can do whatever we want? Eschew kindness, generosity, and any form of empathy? What than does it say about us and our existence?

Our Self-Universe is defined by the people we make place for within it. By the decisions we make based on the experiences others give us and what experiences we give them in turn.

Do unto others as you would have them do unto you