I've spent a few days editing this, but there are still a few things I didn't know how to (or if I should) address.
1) I like the starting section inside Ilyana's apartment substantially more than the later sections. Trying to describe her lifestyle via her apartment's decor was fun.
2) This is supposed to be in third-person omniscient, but I'm having a hard time finding a list of concrete rules for the different POVs. I can say what each of the characters are thinking (and I describe what Peter is thinking, briefly), but does that preclude the use of italicized thoughts? Are those only used in Third-Person limited?