Ds went through a phase round age 11 where he displayed some similar tendencies. This is what we tried:
She is condescending - "what are you getting upset over now?" "What have you lost now?"
Very annoying this one- and ds hasn't quite grown out of it. The only thing, I find, is not to rise to it but calmly say "I am angry because you are not doing as you are told, the way to stop it is to go and do as I tell you now". But calmly. Or ignore his comments altogether but just keep insisting that he does as he's told.
*Constant put downs, every dinner time she finds something to criticise, little put downs all the time, it's like she tries and make me earn her approval
The meals I cook have got to be her liking*
I did (still do) a compromise of cooking a couple of meals a week that I know ds likes: the rest of the time I just ignore him. Maybe a firm "That will do" accompanied by a Paddintong Bear stare at unpleasant comments, but otherwise I didn't let myself be drawn into arguments. He wasn't going to starve, I had no reason to feel guilty, he could eat or not as he pleased, and if he didn't there would be more for me. Fortunately I'm a greedy pig so I can comfort myself with the thought that any well cooked meal is going to go where it's appreciated 
She doesn't approve of my shopping "What did you buy this jam for?"
I might say "well you can always make suggestions before I go shopping and we can take it in turns to have our preference". But then I would stop discussing it as chances are she is only using the jam as a pretext to take out her bad feelings on you.
She steals and lies and then does elaborate theatrics to cover her tracks
Very difficult and not sure I have an answer to this one.
Rude "I want you to wear your hair down, you look ugly with your hair up"
In ds' case it was my coat that wasn't up to his finicky standards. And he was embarrassed if I spoke English in public as that meant people could understand what I was saying. 
I either ignored or used it to my advantage: "Oh you want me to walk down with you to such and such a place- well, it's a chilly day so I'll just grab my warm coat". And in no time at all ds would have shot out of the door with a hurried "It's all right, mum, I can get it myself" and I would be putting my feet up with a nice cup of coffee.
Nice as pie when she wants something, couldn't give a F when she doesn't.
She is vindictive and lies to get me in trouble if I have done something that displeases her. She has almost got me in big trouble in the past with her fairytales*
Thankfully haven't had this one. Sounds very difficult. But if there is a big incident I would perhaps try to work on their sense of dignity and fear of loss of face and gently point out that people who tell silly tales don't do themselves any social favours. Don't overdo it though: fear of face loss is a big reason why they behave in this way; confident people are generally more pleasant.
Constantly angry and resentful
Tick. It seemed to get better when he started Yr 8 and got a better social life/started feeling a bit more confident.
An incredibly huge sense of entitlement
I find only time and patience works for this one. If you keep on not letting yourself feel guilty, not letting yourself be pushed into anything, but not letting yourself get riled either, she should gradually work out that being nasty and entitled doesn't get her anywhere.
"Does chores under duress."
Afraid that goes for most teens and pre-teens. Just keep applying the duress. 
"I find myself feeling so grateful during the short periods when she is sweet and nice. Find myself feeling so grateful when she considers other people apart from herself as it's such a rarity."
Don't. When you feel grateful, you are also focusing on her bad side and the resentment you feel, perpetuating the idea that being nasty is Who She Really Is. Try to stay a bit more neutral, taking any pleasant moment as something natural and normal. Then maybe in time she will come to think that being pleasant is natural and normal for her.
Is as sweet as sugar at school and with friends. I constantly get told what an angel she is!
I think this is a case of counting your blessings. You don't want to be constantly called into school because your dd is the school bully, the child who assaults teachers and cheeks the Ofsted inspector and is on the verge of exclusion. You really don't.