Mutation is a change that occurs in the DNA nucleotide sequence either due to mistakes when DNA is copied during cell division or as a result of environmental factors e.g. UV radiation.
Since all the cells of an organism contains DNA, there are lots of places mutation can occur. However, some mutations are not passed from parents to offsprings and do not matter for evolution. This form of mutation is called Somatic or acquired mutation and it occurs in non-reproductive cells. Hence, won't be passed down from parents to offsprings. This form of mutation majorly occurs when DNA cells get replicated during mitosis or when the cell is exposed to harsh environmental factors that damages DNA strands e.g Ultraviolet radiation.
Mutations are only hereditary i.e can be passed down from parents to offsprings, if they occur in reproductive cells (sperms and eggs). This kind of mutation is called Germ-line mutation.
According to the question, mutations must not always occur in the parents before an offsprings DNA undergoes mutation.
Why is it thought that the majority of natural selection is stabilizing selection? Mutations produce extreme phenotypes, which are selected for. Artificial selection is the most common, which is a type of stabilizing selection. Most mutations are beneficial and produce intermediate phenotypes.
For the environmental risk, it is much better to prevent pollution than to deal with it after it has already been made. When you deal with the pollution, it is hard to say that you can eliminate completely. So, prevention is the first strategy.