I only really have one thing to say: Either hash it all out during discussion- sit her and everyone down- and discuss the situation. Don't constantly single her out as it'll make her defensive and uncooperative (more so than she already is). Talk about how the apartment, in general, needs to have some level of upkeep, etc. Get to the MOST pressing things. Don't try to fight for everything.
For instance, I think the issue with the TV/noise is rather small. GIVE THAT TO HER. Just say that you and your roommates will be more mindful and watch TV with headphones if it's disruptive to her. If you are willing to do something for her, she'll be more willing to do something for you. Or, suggest an alternative: How about if we watch TV before X time, we can watch it without headphones? Etc.
You can't expect her to concede everything when you won't. It doesn't matter how "fair" it is or isn't. It's about learning how to handle people and this is a valuable lesson that, unfortunately, school won't teach you.
Next, talk to her about the trash/recycling. If she can't do it by herself, she should do it with another person. I mean, maybe one of you takes out the trash and she can replace the bag. She can carry some of the recycling things. Or, if she's not willing to do that, she can always wipe down the counters/microwaves every week and, in general, you can use water for that instead of cleaning solvents (considering her allergies, etc).
And, as for contribution: Tell her that she has to contribute something. Ten dollars per month (or whatever) should be enough and everyone can afford ten dollars. It may not be enough to really purchase everything, BUT, remember: Something is better than nothing.
Also, it might already be too late for this, but don't keep arguing/fighting with her. It'll just be a lot of headaches and grief and it'll ruin your living environment. For starters, when you yell/argue with someone, they're not going to listen to you. It doesn't help anything or anyone. IT JUST MAKES MATTERS WORSE. Nobody is going to see "reason" when being yelled at.
I know that this isn't the typical brash American behavior of: I have to defend my rights to x. y, and z. But it works a lot better (from experience). Of course, my personality is vastly different. I don't like to fight with my roommates and, in general, I acknowledge that I am probably just as offensive in some ways I am not aware of. It's just bad to go down that road, but, since you've already gone down it, I guess... you'll just have to do damage control.
Alternately: YOU CAN SIGN YOURSELF OFF THE LEASE. Get your other roommates (and the girl) to agree to sign you off the lease. You'll need to find a replacement and a new apartment, but, at least the problem will be taken care of!
Essentially, there's not much you can really do because it doesn't sound like she's breaching any contract (so I don't think management can do much) and... yeah.
I'm sorry that you're in this situation and it really sucks (I'm going through it right now), but, I think, the most important thing is to change what you want and your perspective. She won't change. Accept at least that much. And know that you'll have to work around it if nothing can be done. 'Coz if you try to get her evicted and it FAILS, there will NEVER be a chance to recover. So... yeah. It's not pleasant/happy/solve-all advice, but... this is sort of the reality of the world, haha. .________.;