Response without reading the rest:
Evolution is the physical processes by which changes happen from generation to generation - mutation and recombination. Natural selection is the process by which these changes happen. At least, most people accept that that’s how these changes happen - there are competing theories by Lamarck (who was writing before Darwin) and others.
Natural selection is about survival of the fittest. This means ‘the ones that fit into their environment best,’ not the strongest, fastest ones, though obviously sometimes the strongest, fastest ones often do have advantages.
In other words, the animals that have features which, in comparison to the other creatures around them, enable them to:
Live a long time after sexual maturity
Obtain a mate
Have successful pregnancies
Look after their offspring well (even if that means choosing the best place to drop their clutch of eggs then leave them to their own devices)
… are more likely to be able to pass their genes on to the next generation.
For example, if the animal lives in an environment where the are are bushes that produce fruit all the way from one foot up to twelve foot up, then the animal that can reach a couple of inches higher than the others around it has an advantage. While its fellows are squabbling over the lower branches our tall guy can strecth up to the extra fruit above. This animal is less likely to be killed in a fight over resources and less likely to suffer from starvation or malnutrution.
The reason for the initial differences between these creatures is that, when genes are copied, sometimes mistakes are made. For example, the genes that keep a young animal growing taller might switch off later than they’re ‘supposed’ to (though that’s a gross simplification, of course).
Creatures that produce sexually have another mechanism for evolution: that slightly taller animal might mate with an animal that also has slightly better depth perception, and some of their offspring will end up with both advantages.
Evolution does NOT mean that ‘everything has a purpose.’ Some features of animals are not there because they offer a particular advantage, but because they don’t offer a disadvantage. Other features might be detrimental to an individual because they’re side-effects of a gene (or collection of genes) which can give an advantage. For example, the gene for sickle-cell anaemia, which gets passed on because carriers also have resistance against malaria.
Other traits - like cancer in old age - persist partly because they don’t much affect whether the individual will be able to live a long time after sexual maturity and so on.
It all takes a long, long time. One creature cannot ‘evolve’ into another - it’s something that happens across the generations.
