Sorry to hear about your struggle with your daughter's behaviors.  Sounds like you have already tried a few approaches to correct her tantrums, etc.  I would like to suggest a positive approach: positive reinforcement.  Instead of telling your daughter that she can't have a cookie now, tell her that she can have it after she finishes her meal.  Instead of telling her to pick up her toys by herself, do it with her.  Set an example.  Make it into a game, and after you are done picking up the toys, admire how clean the room is, how well she did her part, and put a sticker on the calendar.  Explain to her that if she collects 5 stars, there will be a small reward.  Over time, allow her to do most of the work when picking up the toys until she can do it independently.

Pick your battles by reacting to what's important.  If she does not eat lunch, offer a small nutritious snack a couple of hours later, without nagging her about being a bad eater.  She will be hungrier for dinner!  

Temper tantrums are common in 2-3 year-olds, but should diminish over time and go away after age 4.  If they get worse or persist after your daughter turns 4, talk with her nurse practitoner or pediatrician.

Best regards.