I only just finished highschool and the way i understand the whole evolution theory is that yes every particular creature on earth is evolved from another through survival of the fittest. The reason we're not finding millions of different fossils explaining the millions of variations of species is for 2 reasons, it is by pure chance that an animal fossilizes in that it needs the perfect conditions etc, same reason for why diamonds are rare to find, unless the conditions are ideal for an extended period of time, it is highly unlikely something will fossilize.
There is also the fact that the fossils must be
preserved. An earthquake here, tsuname there, the occasional volcanic explosion and all those precious fossils are reduced to dust. Let us not forget that some things do not fossilize as well. Many early organisims had nothing hard enough to fossilize and therefore don't leave remains behind. For most of these we rely on even rarer impressions, fossilized images of a by-gone organisim left behind in some rock.
The 2nd reason is that the idea of evolution is slight changes due to environmental factors, deformities etc etc over generations, but who's to say that one particular primary species isn't able to produce any number of deformities to carry on into generations later so that it contributes to many secondary species? I mean, horses and rhino's are related, so are humans and chimps. The whole point of scientific classification is to track similarities between different creatures and plants and classify them accordingly, but if life itself was such a rare occurance, then wouldn't the sheer number of similarities between these different life forms become even rarer? At some point we need to accept that not EVERYTHING is coincidence, in the case of evolution, considering it all as mere coincidence seems to me like someone is trying desperately to deny one of the few theories about life that might actually be onto something
First off let me say that your reasoning there is faulty. Classification tracks similarities between organisms because based on the theory of evolution, everything came from some ancestor until eventually you reach a singular ancestor to whom every currently existing creature can trace their existence. It's no coincidence, it's a fully known consequence of the theory. We can even look at it in smaller groups. Take the "mitochondrial Eve" and the "Y gene Adam" (before any Creationists get excited, please note these are not the Biblical Adam and Eve).All humans receive their mitochondria from their mothers (although rare cases exist where you get a subset of your mitochondria from your father) and all males receive their Y sex gene from their mothers. So, tracing back as some point a single woman existed from whom all people currently alive can trace their mitochondrial DNA, the same is true for all men currently alive and their Y sex gene. Awhile back the discovery chanel did a special on both people, tracing ancestry down to a time period and location (note that "Adam" and "Eve" where never alive at the same time), don't remember the first but the second was Africa. Also these conditions are flexible. Say all women on the Earth died except for your mother (and if you have sisters them too). Your mother is now the "mitochondrial Eve" because all future humans on the planet will be able to trace their ancestry to her. The same thought experiment works for "Adam" too. Imagine all men except for your father (and if you have brothers them too) died, now all future males will be able to trace their ancestry to your father making him the "Y gene Adam."Moving on to another point, that's the thing, life is not rare, at all. Everywhere it is possible for life to occur, it has as well as in many places we didn't think were possible. Look at thermophilic bacteria, those exist in temperatures that should reduce their proteins to mush and render them all dead, but they live. Our rapid DNA reproduction technology actually relies on the special enzyme variants these bacteria produce to function, without their existence much of our current DNA/genetic reproduction and analysis technology would have just never happened. Then there are the ecosystems that thrive around deep ocean volcanic vents, the temperatures immediately adjacent to these vents cook life dead, but organisims have adapted to live nearby and function without any energy input from the Sun. There are all kinds of bacteria that live in the Antarctic where they should have frozen solid, the solution? These bacteria have developed their own form of organic antifreeze.The only rare thing about life is complex multi-cellular life like you and me. Keep in mind that everything, every plant, animal and fungus exists in a single Domain of life (Eukarya), the other 2 (Bacteria and Archea) are found everywhere and make up the majority of things living upon the planet. So there is no coincidence there, life will occur everywhere it can and it all started out with the same basic building blocks on this planet. From there different selective pressures caused life to change and adapt or perish, which resulted in organisms becoming more and more different until they became a different species. Rinse, repeat over the course of ~2 billion years and you get a myriad of species that can still trace their ancestry back to a single progenitor organism.
Periodically, in a species, certain members will develop certain traits that make them more likely to survive/reproduce than others. These traits are then more likely to be passed on to subsequent generations. Therefore, over time, the species will evolve such that the trait becomes natural, rather than a mutation.
Everything you said is correct up until the end. The first time the trait arises it is indeed a mutation, but there after it is naturally present in the species, just rare. There is no "it evolves to be natural instead of a mutation." The second the trait is circulating about the gene pool and it is natural, the only thing of note is its frequency. This is natural selection at work. The more beneficial a trait is the more the genotype responsible for it takes a larger and larger share of all the genotypes present in the population. Over time it goes from being a rare case to the dominant variant. Over many thousands and millions of years this trait will be reinforced and become more pronounced as new mutations that further enhance the trait are selected as making the bearer more fit.For example, I'll work with sexual selection cause it's easier. A peahen likes peacocks with flashier colors and a bigger, better tail. Those colors and tail probably started as some rare occurrence in the gene pool. However, those traits denote better health and stronger genes, which is how the hens select a mate. Some males had a flashier body compared to the drab hens and the hens noted that there were healthier and better fed, meaning they would produce stronger children. Over time selection for this display forced the genotype responsible to become dominant. Constant reinforcement of this genotype encouraged any peacock that was just the slight bit more remarkable than its peers to be the fittest as his genes were the most desirable. Over the years more and more successive mutations would accumulate until you get peacocks as they are today. Various bird researchers have tested out adding frills to males (of any bird species, not just peacocks) and have seen that birds naturally are attracted to flashier males and take it as a sign of good health and good genes.