Is there an "Adam and Eve" for each new trait during (not just human) evolution?
For most traits, there is no clear line where the trait is present or not. Exceptions are traits that occur with a single mutation, like lactose tolerance. So to pick one example, you had a population of fish that had a lung-like organ, and that by genetic drift that organ got more lung-like in a sub-population. So for most traits, you have a combination of mutations that lead to the traits, and these mutations need not occur in a direct line of ancestors. (I.e., a descendant will combine independent mutations from its parents.)

So there is no "Adam and Eve" in the sense that these are the only ancestors of all living individuals of a species. This would be a terrible genetic bottleneck! See this illustration, which comes with the estimate that the population size of the chimp-human ancestor was around 100,000. 



You ask for "a first dinosaur with feathers who is the father or mother of all birds". It's possible that feathers arose multiple times from the same feather-like structures, or only once. But it is clear that this first dinosaur is only one of many dinosaurs that lived at the same time, and who are also ancestors of all birds. 

Further reading: Lactose tolerance evolved several times independently (see "Convergent adaptation of human lactase persistence in Africa and Europe.").