Working out in a fasted state has some benefits if you want to build strength/muscle (ie. increases HGH), but you should go all day without food (not eat carbs for breakfast, etc) to take advantage of it.

On days I workout:

7am coffee (black no sugar)
4pm workout for ~40 mins
6pm dinner - 2lb of meat

Cardio is a waste of time and effort (unless you are training for a specific cardio event).  Get into the weights (even just do push-ups and pull-ups) and drop the cardio.

I do on workout day.  The day after working out I just eat whenever I am hungry.

Other days are one or the other depending on how I feel.

You're not eating enough.... not even close... unless you're eating an entire chicken for dinner

I workout before eating...

I workout during fasting, I have read everywhere that you aren't supposed to run on empty, but I ytry to think the paleo way, and I think Mr Flinstone would have to go out at empty stomach to hunt for something edible if he needed it.
I know I cannot workout at full stomach because I'd vomit it all (lol, it's graphic, sorry) my workouts tend to be violent more than intense and I wouldn't be able to keep anything down.

Chicken breast is probably one of the worst choices for someone following Paleo. You need fat on your meat.

It depends how you make it! Steamed? Yes, I agree with you. Sauteed in lard? Great!