Mutations happen all the time. However, mutations are always disadvantageous and result in cancers and tumors. This is because you only need one thing to go wrong for a harmful mutation and you would need thousands (tens of thousands) of things to go right in one particular cell to produce an advantageous mutation.
Humans lose the ability to produce lactase as they become adult, thus becoming lactose intolerant. However, there are two single-point mutations, each of which are able to prevent this, resulting in lactase persistence. One of these mutations, stemming from around the time of cattle domestication, is virtually universal among North-West Europeans, but the occurance of this mutation decreases in a radiating pattern, as can be seen in this map:
imageYou may notice that there are other areas where lactase persistence is common - all of them areas with heavy pastoral backgrounds.
It would also have to be in a reproductive cell to be heritable.
…Yes. That’s exactly how it works.
Indeed, the germline has a special process for actively producing even more novel gene variants called recombination.
You are starting the cycle at the wrong position - it begins with the egg, not the chicken. A beneficial mutation in a gamete results in both a somatic line developing an individual that can benefit from the mutation and a germline that produces gametes that have the potential to carry the mutation into the generation, which is more likely to happen due to the individual benefitting the individual.
Also, the effects that a somatic-line mutation can have are limited, especially post-embryonally, anyways, as only so many cells, and more importantly only specific types of cells, will descend from that cell.
In the 150 years since Darwin no one has observed a single favorable heritable mutation.
Besides the fact that this is not true - see for instance the nylon-eating bacteria already mentioned by Malingspann -, one hundred and fifty years is a very short time in the scheme of things.
Creationists claim that their book, speaking of a God far beyond the scope of human experience, indeed, of whom it says that a thousand years are but a day to Him, teaches them humility in being mere mortals. Yet in truth, their horizon is so painfully narrow, their perspective so awefully anthropocentic…
In 150 years how many species have gone extinct versus how many new species have been created.
And this is OUR fault - our collective greed and selfishness and callousness destroy countless habitats, unleash manifold forms of pollution including a massive abrupt climate change that are already causing considerable problems not just in some poor country you could not care less about but also in the so-called developed world and indeed actively overhunt several species for really stupid reasons!