1) Current US health/diet regulations state that 1 whole egg a day is a-okay. This is trending upwards from the previous amount. Honestly, even more than 1 a day can be just fine, but as with anything, there is a point where excess is detrimental.
Well, the US Health/Diet Advice isn't really based on good science. People should really be eating eggs everyday over breakfast cereals. Eggs are great nutritionally speaking when it comes to a complete amino acid profile, vitamins and minerals that are actually bio-available and active, and have a really good fat content ratio. They're high in saturated and monounsaturated while keeping the ratio of polyunsaturated omega 3 to omega 6 relatively in safe ranges. They're also one of the few food rich in choline, which women and children should really be getting in their diet.
The only time eggs become a problem is when people do stupid things to them, such as removing the yolks and keeping the egg whites to make a so-called "healthy omelet" in which all the egg whites do is strip out the biotin out of your body and create deficiencies.
2) "Meat" is a broad term. A lot of shit that is added in processing can be bad, that's true, but it's not universally bad just because it is processed.
True, the processed meats usually has white flour attached to it (corndogs, buns, pizza doughs etc), which are definitely fattening and cancer causing.
3) Nuts being "pure fat" is simply wrong. They're also a good source of non-animal protein. Besides, not only is the fat in nuts natural (aka, not falling under your "processed" concern from #2), but they're also overwhelmingly poly- or monounsaturated fats; only a small amount of saturated fat and no trans fat.
The only problem I have with nuts is that they have an incomplete amino acid profile and are high in polyunsaturated fats. While the omega 3 polyunsaturated fats are good, the omega 6 polyunsaturated fats are not, especially in the quantities most Americans consume them in. What will make nuts bad for you is when you cook or bake them in high temperatures. This causes the unstable polyunsaturates to break down and release unpaired electrons that will cause all kinds of inflammation in your body. Also, some nuts such as macadamias, contains omega 7 trans-fats which are actually good for you.
Besides, contrary to popular beliefs of the late 80's/90's America, fats aren't bad for you if you choose good ones and don't eat a huge excess... of course, those modifiers can be applied to any food.
Indeed, it took the government 30 years to admit that trans fats in hydrogenated forms are bad for you; it'll probably take them another 30 years to admit that saturated fats and omega 7 trans-fats are healthy and good for you.