I have been exploring there for week, but nothing is happening. I feel like I'm going in circles! Is there a certain order you need to enter the mirrors or something?

Yup! Every room has a description. For example, it will say the walls are sapphire, amethyst, silver, etc. You want to follow this:

There is a Sylestia Walkthrough that you could look at too. It includes the genetic scans of bosses, secrets, and pretty much everything else.