Why sun rays don't burn our skin?
The reason that UV light causes sunburn, while normal light does not, is not founded in the energy carried by single photon. As stated on wikipedia:


  Importantly, both sunburn and the increase in melanin production are triggered by direct DNA damage. When the skin cells' DNA is overly damaged by UV radiation, type I cell-death is triggered and the skin is replaced 


The UV light can cause reactions in the DNA of the skin cells that directly damages the DNA. A low amount of this damage can usually be repaired by the cells, but a lot of DNA damage will lead the cells to die and cause inflammation reactions in the skin (the sum of which is then what we experience as sunburn).
[Here is a citation also explaining this, the paper is behind a paywall though]. 


  What area of skin is necessary to absorb one single photon? How many photons of visibile light per cm2 are required in order to produce burns to the skin?


A single UV photon has no measurable size and can therefore in principle be absorbed by any arbitrarily small patch of skin. In practice only those photons that interact with the DNA in your skin cells are relevant for sunburn (that will be a very small fraction of all UV photons). Additionally the melanin in your skin will also absorb photons and therefore protect the DNA from the UV radiation, which is why people with darker skin get sunburn less easily. This also means that the amount of radiation/skin area required to cause sunburn varies from person to person and can be influenced by the ability of your skin cells to repair the induced DNA damage.