For the sleep thing, you could try putting her to bed a half hour earlier than when you currently try to get her to bed. Or even a whole hour. Sometimes when they're too tired, they have trouble settling. Also, is she still taking a nap? You could try giving up the nap if she is napping so she'll sleep earlier and better at night, and conversely you could try getting her to sleep a bit in the afternoon if she isn't napping anymore. If she really isn't tired until 11, it might be that she doesn't need a nap yet, but if she's getting overly tired, getting some sleep in the afternoon might help. Sleep issues sometimes involve trying several things to see what clicks, and sometimes what clicks seems like it would be counter-productive, like getting them to sleep more and earlier. But there's a saying, "Sleep begets sleep."
That might make everything improve, because tired kids are cranky. If she's not tired anymore, you might find that she's happier and doesn't fight as much.
BUT . . .
At some point in the toddler years, but often I think when they're 3, kids start wanting autonomy. They figure out they're different and have power over themselves and they want to exercise that power. So things that didn't bother them start to bother them. They used to be happy having you constantly telling them what to do, and now they want to decide for themselves. My advice would be to give up whatever you can give up. Put only weather-acceptable clothes in her drawers, and let her choose her own clothes to wear, even if they look funny to you. If she doesn't want to wear a sweater but you think it's cool, don't make her wear it but bring it with you in case she changes her mind. Let her wear her fancy shoes instead of the practical ones when you go out (and you can bring along the practical ones in case you end up at the park.) Put her dishes in a place where she can get them when she wants them. Put snacks appropriate for her in a place where she can choose what she wants and get them for herself when she's hungry. Whatever autonomy you can give her, do. And if you start into a power struggle, ask yourself what the worst thing is that could happen if she got her way, and if it isn't too bad just let her have her way.
That does a couple of things. First, as she gets a feeling that she has some autonomy, she will lose the feeling that she has to fight to get it, and she should stop fighting over things as much. And the the second thing is that if you're not fighting about all sorts of things all the time, you will save your strength and sanity so that you're able to fight over the issues that are really important and where you can't budge, like sitting in the car seat and that kind of thing.
So I'd try the sleep thing first and not worry terribly about the autotonomy thing at this point unless getting more sleep doesn't solve it. But keep that second part in mind for when she does start wanting some control over herself. And if sleeping better doesn't solve everything, then the autonomy issue might be something to consider, although she seems young for that.