that all sounds very familiar, and my local university cooperative extension service had a helpful PDF file on Ages and Stages that described the 3-to-4 challenges perfectly so far as my experience with a DD also about to be 4.
I use standing in a corner 3 minutes as a punishment, and then she has to do whatever it is anyway. I also use corporal punishment judiciously, which hasn't been made a crime -yet!- in my state, but the hysteria always spreads. Not that I condone child abuse, but I don't agree that all corporal punishment is abuse. Abuse can be physical or verbal or psychological, but I think that calling all corporal punishment abuse is like calling all speaking verbal abuse. My opinion and a tangent though. My DD also tried bargaining and telling me she would rather stand in the corner than pick up her toys, but when she learned that standing in a corner still meant she had to pick up her toys afterward anyway, she quit that business. As for going without dinner, if the kid is hungry, she will eat, and if your DD really doesn't want supper, I guess I would allow her not to eat it, although when mine pulls the "I don't like/want that" whch is a recent thing, because she has always amazed other people with her willingness to eat raw broccoli, cooked spinach, pretty much everything... I tell her she doesn't have to eat it but I am not cooking her something else, and I tell her that she doesn't have to finish it, but she needs to eat one bite of each thing. That usually triggers her into realizing she's hungry and she will eat a decent portion.
But she's not that tough a kid, and I think at this age they are really seeing how far they can go in terms of bargaining and pushing limits. Little rules lawyers. A friend coined the term Justice League to describe all the rules lawyering they do at this age.
Hope you have success, at not letting her turn eating or not eating into a bargaining chip with you. They say kids won't starve themselves, and they need to find out that they can't get a big reaction out of you by refusing to eat. My attitude is "Oh? I am sorry you don't like it, because it will be harder to eat it." DD:" I'm NOT going to eat iT!" me: " Oh dear, I guess you'll be hungry then." And whether she eats or not isn't the big deal, but if she says she's hungry later or asks for something, I say "Oh, ok here's your dinner now that you are hungry."
I also give everyone room to have a few aversions, because I HATE beets and almost can't choke them down, and DH gets nauseated at bananas and winter squash. But that isn't the case with DD saying nearly every night " I don't like ____" when it's something she eats all the time. She also refuses to take baths