A.Q.
First off, my kids both started eating very little right around their second birthday. I just keep snacks that they could grab throughout the day. They can get to the yogurts in the fridge and fruit on the table. Then from time to time I would put out a few cheese stick and crackers. My ped said that as long as they were having healthy bowel movements, than they were eating more that I knew. Also remember their stomachs are only the size of their fist. So they can't fit that much in there at one sitting and need to snack more than we do as adults to get the proper amount of nutrition.
Now the behavior also sounds familiar. It is something that has cropped up from time to time with my oldest. When she starts the crying because she doesn't want something, simply take it away and walk away from her. Don't give her what she wants, just walk away and leave her there. If she wants something, tell her you can't understand her when she cries and you really wish you could help her, but she will have to talk in a normal voice so you can understand it. If she continues to cry, just say, "I don't understand. Normal voice please." and walk away until she can come to you with a normally vocalized request. It's hard and it takes time, but she'll get it. And if you are consistant, she'll figure out that the crying doesn't get her what she wants as well as words. My daughter is 6 now and when it does crop up again, which it has recently due to her copying behavior she has seen in a classmate, I just ask her, "Does crying get you what you want?" Magically I hear her normal voice seconds later.
It's not easy and it will take a couple of days for your daughter to break the habit. But at this point, that's all it is. A bad habit. Good luck.