It is widely suspected that the anaerobic bacterial species Propionibacterium acnes ( P. acnes ) contributes to the development of acne, but its exact role is not well understood.  There are specific sub-strains of P. acnes associated with normal skin, and moderate or severe inflammatory acne.  It is unclear whether these undesirable strains evolve on-site or are acquired, or possibly both depending on the person. These strains have the capability of changing, perpetuating, or adapting to the abnormal cycle of inflammation, oil production, and inadequate sloughing of dead skin cells from acne pores. Infection with the parasitic mite Demodex is associated with the development of acne.   It is unclear whether eradication of the mite improves acne. 
Sunburn is inflammation of skin caused when it is overexposed to ultraviolet rays of the sun. Though both UVA and UVB rays are harmful, it is ultraviolet B ray that is more damaging to the skin. With growing awareness, people have started using sunscreen to protect their skin. Most of the time they apply sun blocking agent on legs, hands, arms and other parts of the body that are exposed to sun. This they do it to prevent melanoma the deadly skin cancer or skin wrinkling and lathering. However, people often forget to apply sunscreen on their face, and the result is sunburned face.
Well, generally, the person who states a link exists is usually the one who should prove it. It is incredibly difficult to prove a lack of difference.
However, I will refine my statement. There is no evidence in the medical literature that there is a link between diet and acne. There are few studies, but the ones that have been done don't prove an effect. I did a quick search and limited it to pubmed articles available for free.
Here is a review article:
Here is another article. Even though this study is flawed and very small, it shows no link between diet and acne (but it does show a link between weight and acne):
Considering insulin's role in acne is interesting, but it is only a hypothesis, and not a very well supported one. The authors of one article cite polycystic ovary syndrome as an example of a disease with high insulin and acne. However, there are other diseases with high insulin which are not associated with acne. I seriously doubt insulin elevation causes acne, it is probably something else. PCOS patients for example are usually obese.
I respect your enthusiasm and intellect, but you are on the wrong track with this article. Please be careful when you give people medical advice unless you are a trained and licensed physician.