A typical burger meal is definitely processed food because the meat is processed mechanically and mixed from different sources (usually with added fat); the bun is made from refined flour and refined oils; and the fries are thinly-cut potatoes blanched and fried in more refined oils. (Not to mention a whole bunch of chemical additives which are the norm rather than the exception; and "hyperpalatability" tweaks which means the food is formulated to taste unnaturally good.)

You could perhaps argue that a home-made burger meal made using whole cuts of meat, a lean wholemeal bread dough, and potatoes roasted in animal fat could count as a healthy/whole food meal, but it would taste different to the typical hamburger meal we all associate with fast food.

Fast food also has an enormous marketing industry behind it which pushes it in unhealthy volume, with maximum convenience, and at (until recently, at least) affordable prices.

Yes, this is all junk food. It's not that difficult.

Eaten in moderation these things are fine. But they are highly palatable calorie dense meals that are not great for you over time and in huge quantity. A burger is generally speaking a burger, regardless of how fancy. Deep fried stuff is deep fried, regardless of the cut of the vegetable or how organically it was grown.

Your latter question is far more interesting to me. I don't have a solution for that really. Society gets what society demands. I don't know how you'd fix those incentives without seriously horrible second and third order effects.