I´m not sure if the survivors of mass extinction episodes fit well as naturally selected; yet that is semantically arguable that it would be a sort of natural selection, in population genetics it would be more adequately considered bottleneck effect or founder effect, unless, whatever the factor of mass extinction was, it made possible to organisms with some very specific set of traits to survive. I.e., some radiation-resistant bacteria would be truly selected in this scenario of increased radiation, but those that survived simply because had the happen of not having highly deletereous mutations caused by the radiation, are not being selected according with the jargon; it was a matter of luck, there was no "merit" of any trait in the survival. Eventual beneficial mutations conferred by this raising of radiation would be considered to be naturally selected or not according with the difference that it made to a certain trait, comparing with the normal, non-mutated trait, in its adaptation. Again, this individual that was twice lucky is not considered to have been selected by the radiation event; the radiation event more frequently does not select, but sorts, unless it´s something about radiation-resistance.
Depends on the concept of the species in each case... there are species, which are more properly called ecological species, which can yet interbreed with closely related species and generate fertile offspring. They differ more in some specific adaptative traits, adapted to a certain niche, and are "ecological" species because of that. Galapago´s finches, and lots of bees are examples. That's why almost all the American bees are africanized bees, because African bees were brought to South America and accidentally spread along the continents, crossbreeding with local varieties.
Natural selection is primarily the cause of adaptative change; populations that evolve different adaptations may eventually, gradually, became less fertile with each other, both because the populations do not need to interbred anymore and differences interferring with the viability between hybrids are not selected out, and because further diverging adaptation may actively hinder the hybrid viability. Then the fate of ecological species, if teared apart by adaptation enough, is to become trye biological species.
At the same time, physiological speciation, where one species cannot breed producing fertile offspring with related (biological, not ecological) species, can occur just by chance, not preceded by adaptative change, and retain two barely changed biological species made out of one. They may be ecologically forced to divert adaptatively then, or one of them could become extinct, if they´re adapted to a very specialized niche and still inhabit the same (limited) habitat.