Please answer! What roles do genes and mutations play in cancer formation?

Absolutely central. All cancers are caused by accumulated genetic mutations that remove proper controls on cell growth. The more aggressive cancers usually have acquired mutations that themselves destabilize the genome, allowing more and more aggressive clones to be selected for. Any "cause of cancer" that doesn't involve something that mutates genes or increases selection for mutations will prove to be bogus.
An important one! Many cancers have specific gene mutations associated with them, that , if present, aid in their diagnosis. The more we find out about cancer, the more gene abnormalities we discover. Some are due to genes we inherit, but most are due to mutations that occur over our lifetime.