For soft-bodied species, fossils are rare because the soft body parts don't fossilize very well.
Any biological family is a branching family tree. We often have one or two fossils on one branch and another from a different branch and some more from still another branch. We then have to figure out what is ancestral to what and what is just a biological dead end.
It helps to think of species like individuals on a family tree. A grandchild species has a parent species between itself and its grandparent. Two cousins are on different branches and are not direct descendents of each other, etc.
It's that an organism changes to suit the environment it's in to become another organism better suited to that environment, or something like that?
In practice, only a slight edge is needed. If a characteristic allows its owners to have 1% more descendents than those that lack the characteristic, it will eventually spread through the entire population. Evoltuion is more about populations that individuals. It's survival of the fittest population, not the fittest indiviual.