Re: Is this skin cancer?
I can certainly understand your father's hesitancy in seeing a doctor. Why go to a doctor and possibly hear bad news, when you can not go and live in blissful ignorance? The problem is if your father has either squamous or basal cell cancer, these can eventually become fatal if left untreated. Let me explain it this way:
Melanoma is the least common of skin cancers, but one of the fastest growing and most aggressive of skin cancers. If left untreated, and melanoma reaches stage IV, average life expectancy is 6 - 9 months.
Basal cell and squamous cell cancers are slow growing cancers. They can inhabit the skin for years without threatening one's life. They might grow bigger on the surface, but it takes a long time for them to grow deep enough to affect the lymph system, which is how skin cancers spread. Melanoma (especially nodular melanoma) grows quickly and can reach the lymph system much faster, which then spreads to the lymph nodes and then onto other organs. Basal & squamous cancers don't grow that fast.
However, if left untreated, basal and squamous cancers do grow - they are cancers, after all. And if left to grow, they will eventually grow deep enough into the skin to affect the lymph system. There have been deaths attributed to both of these cancers, just not in the numbers of, say, melanoma. How long does it take either of these two cancer to grow to the point of reaching the lymph system? It varies from person to person. But this I can tell you: death from skin cancer (or any cancer, really) is not a pleasant experience for anyone.
There is also the appearance of the skin. I'm sure the lesion on your father's face is probably bothering him. The procedure for a biopsy might be a little painful, but is it worth his life? And there is a possibility that it might not be cancerous at all. In that case, whatever this is would be gone and he would no longer have to deal with it.
I hope you can convince your father to see a doctor, if just for a consultation. A lot of doctors can tell by looking whether something is to be concerned about or not.