Apart from you removing the quote coding and thus not making clear to people skipping to this page that you didn't write this, glad to see I can still make an impression.
Side note this is wrong all kind of levels and Rei in my view is not submissive she is quite out of fear and terror of being replaced it why she does not value her existence or life and her apartment being a mess points to someone with deep depression, hence the bloody bandages and things left as they are not picked up.
Rei isn't afraid of being replaced, she knows she's replaceable and has resigned herself to that fate. That's why she's willing to take suicidal missions, because she knows her death is no real loss. As for her apartment, I think that's more to show her detachment from the world, like the way she isolates herself with books. She's not truly depressed because she's capable of being happy, as seen with Gendo and Shinji. She's more withdrawn than depressed.
And it's pretty clear she's submissive. Apart from accepting any order without question, there's that time she didn't even try to stop Asuka from slapping her.