No worries Arcy... you’re doing the best you can with what you have. The burgers might not be the best choice as far as meat goes because most of the institutional burgers are made with soy and different fillers instead of real meat. If you have other options, you might be better off (chicken, pot roast, exc).
Keeping chicken handy is a great idea... I do the same thing. Cook up a bunch of drumsticks and keep them in the fridge for a small meal or a snack. Keeping the skin on and eating the fat is fine if you’re able to get organic chicken. It's a great way to get extra fat into you diet. If your not able to get organic chicken, it may be better to trim the fat and remove the skin because that's where a large portion of the crap (hormones, antibiotics, exc) are stored in the animal. The less you can consume of this crap the better.
As far as eggs go... EAT THEM! I do the same thing with eggs that I do with chicken... hard boil a dozen at a time and take them with me to work for a snack or a small meal. In an average day I'll eat 8 to 10 eggs... maybe 4 or 5 for breakfast and 4 or 5 for lunch/dinner. They are a great source of protein and amino acids and they are one of the only foods to contain naturally occurring vitamin D. Eat as much as you want.
Your off to a good start... keep it up. And as they always say... there's no such thing as a stupid question.