When a friend tells you you can try their food, is it rude to take a lot?

It was very rude of her to do that. I've had friends do the exact same thing. I've learned you just have to say, in a joking, but firm tone of voice "Hey, get your own", then smile at her and pull your plate closer to you. If she doesn't stop after that, tell her "Cut it out, I'm starving", but smile. You don't want to lose your friendship over a plate of food, but you can't allow yourself to be a doormat. You teach people how to treat you, after all.