It's been a few years since I took a class in the biology of cancer. So, I am not a speciallist either. But I also read science magazines frequently which kind of updates my knowledge of the subject.
I don't remember reading about the connection between inflamation and cancer, although I do remember that people with some inflamatory processes such as irritable bowel disease, are at a higher risk. As far as a higher reproduction rate of the cells being linked to cancer, the only reference to that that I remember was in some cancers typical of children, in which it was speculated that the reproduction rate of the cells was connected with the elevated risk for those cancers.
One of the concepts I vagely remember from my class, was that cancer is a complex process that takes many steps to complete. With respect to cancer agents, I remember talk about a promoter and an initiator. One of these kind of created the conditions necessary for development of cancer and the other trigered the process. I think I remember then talking about a one-two punch.
I also remember that there was something that was considered as a background cancer rate, which was not attributed to artificial causes. As Tavi says, there seem to be insuficient or no studies segregating the different causes of this background rate. I don't remember if a genetic predisposition was included in that rate or excluded. Things like cosmic rays, to which we are all subject, would definitely contribute to the background cancer rate.
Talking about causes, it appears that oxidative (free radicals) can be a cause of cancer and this is one of the reasons a lot of attention has recently been given to antioxidants. (green tea, vitamins C,E , lipoic acid, flax seed, fruits and vegies). Oxidative damage, together with inflamation has also been linked to artherosclerosis and diseases of the brain such as alzheimer's and parkinson's.
With respect to radiation, I think I read recently that slow electrons can produce a lot of damage ( this would be from a new study). I think it was previously thought that in order for a free electron to produce damage it needed greater energy.
So, in summary, an electron, a cosmic ray or ionizing electromagnetic radiation (X-ray, gamma) can somehow damage the DNA, producing a mutation that initiates the cancerous process. But it looks like chemical agents that produce oxidative damage are as important or maybe more important than radiation in their oncogenic properties.
It looks like the cells have mechanisms to repair the damage to the DNA. This mecahnism does not always work. But a good intake of antioxidants may help.
It may be very hard to avoid radiation. In the case of the sun, the most dangerous type of skin cancer is melanoma, which is often the result of bad sunburns when you are young. There is a debate between dermatologists and other doctors as to how much sun exposure to get. It happens that, especially for people with dark skin and those living at high latitudes, a lack of sun may be even more negative because it results in a deficiency in vitamin D. There are recent studies that suggest a dafficiency of vitamin D has vast consequences for your health which were not recognized before.
I think it is always good to be informed about possible environmental dangers for your health, including sources of radiation. But it may be best not to worry too much about this as in most cases there is little we can do about it. But we can try to eat a healthy diet that includes fruits and vegetables (read about those that offer more cancer protection, such a broccoli) , take a multivitamin suplement, exercise and avoid cigarette smoke. (passive smoking may be as bad as smoking the cigarettes yourself). And don't forget that heart disease is the main disease causing death. A healthy diet and exercise will protect you from both to a certain extent.