Ok so doing a tattoo on a beauty spot can't devlop a cancer right? Its just the fact that its harder to detect if the beauty spot became cancer right?

You got it. The tattooed won't be any more likely to become cancer, whether or not it's on a "beauty spot" (birthmark). In fact, the dark colors in tattoos make skin cancer slightly less likely! but if it does appear, it might be harder to find. The good news is that the vast majority of birthmarks have no additional cancer risk. The exception would be congenital giant melanocytic nevus.
Probably not. It depends on what you call a beauty spot. If this is a birth mark that has not changed throughout your life, i would say you are unlikely to have a problem from it. However, if it is a multicolored, irregular lesion, tatoo or not, i would say you should have it checked by your doctor for possible disease, like melanoma. Having a tatoo has its own risks as well. See your dr. To be sure.