I got news for you: Rich Fronning, Dan Bailey, and all the other elite men and women of crossfit did not get where they are in their athletic careers by doing crossfit. They all got strong first, doing squats, deadlifts, etc. They didn't do more weight than they could handle for time (at least not at first) with crappy form while not eating. To poorly summarize an analogy from Dan John, strength is a glass that holds all your other athletic ability. The stronger you are, the bigger the glass, and the more potential you have. The stronger you get, the better you will be at crossfit, and crossfit will not get you as strong as you can be.
Another answered a similar question of yours here and answered it well.
Additionally, you need to keep eating good food. Chicken breast isn't fatty, and is full of protein. Eat that if you're worried about fat in meat. It's fine to supplement with amino acid whatever and protein shakes, but the main meat of your meals needs to come from, well, meat. You can't live off vitamins or supplements, it's not healthy and won't help you achieve your goals.
The jury is still out on running. T-nation, while certainly biased towards the strength and meathead crowd, has a few recent articles on running and other LSD (long, slow distanec) workouts. People who run will tell you running is great.
Death of Steady State Cardio
Regular Cardio will Make you Fat
Do take whatever anybody says with a grain of salt. Try some things yourself and give them time to work. Clearly crossfit isn't doing it for you. Take time off from crossfit and focus on getting strong. Come back after a few months, and I'll bet you will see that you are better at crossfit.