Sure, but with sufficiently many people, these effects will usually average out. I'm not saying the situation is great, but it's still an important field of study and we need to make progress in some way.
In the case of dietary studies, not really. There are a few factors which are known to have a big effect on your health--being wealthy, active, and moderate in particular--and a lot of the big studies are really just uncovering yet another proxy for those factors.
Of course, you can turn that around and make the realization that your diet doesn't really matter: there's no diet that will magically make up for being a couch potato. And outside the main well-known interventions (e.g., eating less calories), the solution is generally to just be more active and things like that rather than trying to tweak your diet.
No they won't. If you have two correlated factors and only measure one of them you can easily get to totally wrong conclusions.
If you have a food that is more often eaten by people doing a lot of sports, you will measure that eating that food is correlated with being more healthy. But it would obviously be fallacious to conclude that this food is more beneficial to health than other foods.