She isn't showing up in the loading screens and it's locked up on me once already while in a training sequence. 
Is this normal (apart from the crash) or is my copy defective? I've installed it to my hard drive and it hasn't seemed to help.

I should probably also say that I'm playing the Xbox 360 version.

Sounds like a defective copy to me.

Yeah I think you got a defective copy, don't worry, you can probably exchange it.

She doesn't show up in the first few loading screens for me either, first chapter onwards she does.  I'm pretty sure it's intentional.  No crashes here though.

so when I play the demo, the game crashes like every 2 minutes--literally. I just got the game in the mail today from amazon and it does exactly the same thing. I haven't found many other issues like this, and I'm starting to think it's a problem with my xbox...
 
also, I get the sense the not-showing-up in loading screens is intentional for the first few, but I havent been able to get past the first part because the game crashes constantly (and not in any particular place).

Sounds like you have a defective copy.  I have the game installed to my HDD and it works fine.  At first she doesn't appear in the loading screen until later like Chapter 1 I think.  If you are still having the issue, get a new copy of the game.