At what point do scientists consider an animal a new species?
That depends on who you ask. A geneticist will say that it is when it can no longer breed with other species to produce fertile offspring. He will also have the hubris to call it the "biological" species concept as if the others were not biological. Pure BS. It is given the lie by rassenkreissen (ring species) and by fishes that breed freely across generic lines, as well as species. I prefer C. Tate Regan's definition, that a species is whatever a competent taxonomist working with the group considers a species. It sounds flip but it is what most of us use most of the time. And it works. My major professor found that out when he disagreed with me in print and got shot down by at least one reviewer.
Two animals are of different species if they cannot breed together and produce viable offspring. At least, that was the plan for the word "species". In practice it is quite difficult to determine and many errors occur.
They do not. There is no such point. Ultimately, it has to be the judgment of experts as to whether a particular population is a new species. There is not a list of characteristics for defining something as a new species. You cannot simply say you tick all the boxes so you are a new species.