Cheese:Most of the commercially available cheese products contain a lot of saturated fat, yes. This is not really good in mass quantitites. A slice or two in a sandwich will not kill you, but do not use it as main calorie source.Low fat cottage cheese is your friend if you feel 'cheesy' (protein + calcium)
Out of a single cell of an egg a complete, living organism can grow. I personally believe that egg is literally the only food source which contains every single building block to build complicated organisms like a body of a bird. Or a human... (Obviously you are not eating the shell which is the main Calcium source for the little bird's bone development, but otherwise..) I eat eggs every single day. If you are worried, eat 2 whole and 5-6 whites. All of the fats are in the yolk, the white is the purest form of protein you can get.
Cholesterol:There is a lot of confusion about this topic since cholesterol have been labelled as an evil thing. In fact there are multiple types of lipids called 'cholesterols', and half of them are healthy / vital. Plenty of sources on the internet, Google it. Since you are probably training hard, your veins are just doing fine. Obviously if you are having some sort of a condition, check it with your doc.