Eating food high in fat, sugars and carbs is bad for skin and causes hair loss?

No. You need to stop reading disinformation websites. Now, people tend to overeat greasy and sugary stuff and that's how they get fat. The public therefore comes to believe that this stuff is "bad for you" and people are ready to believe that is causes other problems as well. In fact, acne & most other skill trouble is mostly unrelated to diet, and balding is hereditary.