What? No. Everything evolved from the last common ancestor of all living things to what they are today. A "species" is a label that we put on groups of animals. Not completely representative of the natural order, it is by and large a good way of identifying and distinguishing populations of mutually reproducing organisms. (For example, ring species, and hybrids show that there is no perfect correlation between the species label and what they represent.) It are the most specific of all the taxa (hence "species").
Plants started as plants and continued as plants. Animals began as animals and continued as animals. Humans began as humans and continued as humans.
Well, first, humans are not separate from animals. Humans are animals; African Great Apes, specifically.
Next, (although this is grossly simplified:) You've also forgot to mention fungi (among the Eukaryotes), bacteria and a bunch of other stuff. The ancestors of each of these Eukaryotic lineages found different, specific ways to be reproductively successfully. There was, however, a common ancestor to plants, animals and fungi. None "started" as plants, animals or fungi, but evolved into creatures whose descendants we classify as such.
I'm not sure I follow your point.
My point is that if you concede that animal populations adapt to their environment by having differential reproductive success, you've conceded that natural selection has occurred. There is nothing which stops variation within a species from producing a new species if it provides for a reproductive advantage.
You think the great apes are the ancestors of modern humans? Which humans?