You are correct not to eat your meat raw. The protein content of meat won't change from cooking. It will lose some fat of course. Keep your diet varied. It's risky to just eat a couple of foods. Use different meats, eggs, veggies, salads.
Fitday.com has a lot of different foods with their ratios calculated.
It's better to eat regular meals than to not eat for long periods. It keeps your metab cooking along.
If you are going to the Y in the morning do your weight training first, follow it with cardio, then have a nice meal right after. Protein drinks are good to throw into the mix. When combining your workout like you do, it won't hurt you to have a decent small meal 1 hour before.