I think it sounds like you are doing a fantastic job from what you described. You are right about encouraging the vocabulary, temper tantrums can stem from communication frustration.
In my opinion, it seems like this is pretty normal developmental stuff. Personally, I would stick to your guns (if the tantrum is over being told no), and let her see natural consequences (If you throw food on the floor, you don't get to have it at all). I bet you'll find that if you don't let yourself be too upset by the behavior, it will pass on it's own. Do what you can to accomodate her feelings (you can try to hold her, redirect her etc to calm her down) but if she just wants to kick and scream--let her. Soon she'll realize that that isn't going to get her anywhere. As her verbal skills develope, she can begin to learn to ask for things in a nice way. Of course, this lesson will take years. I'm still working on my daughter who is 2.5. She is much more vocally demanding then my two older boys were. (they are 8 and 5 also!) Maybe it's a girl thing? Maybe it's a youngest thing? Who knows.
You'll be ok, mama. You're doing great!