assume wyverns are either mammalian, prootomammals, or avians. they have wings, three digits on the end of each, use fire breath (reacting hydrogen and oxygen or some other smokeless burning/explosion in the nostrils), have limited social behavior, and lay eggs. How reasonable would it be for them to evolve on earth as soon as possible after the Great Dying? what impact would this have? I'm okay with them not resembling wyverns much, so long as they meet the conditions.
This question has been asked here many times before. The answer is that it's biologically feasible so long as the wyverns are considerably smaller than they are depicted in fiction. Expect them to be roughly the size of an Andean condor, perhaps a bit smaller. (while there have historically been larger flying animals, a wyvern's body shape precludes them from reaching those sizes.)
As for the impact on evolution, many more animals would naturally look up more often. With fire breath, these wyverns could theoretically take down prey much larger than themselves... especially if they produce a sticky, flammable bile that allows them to shoot "sticky fireballs" at targets, resulting in a long and protracted burn.
For the prey animals, the response is much the same as without; run, and hide in dense forests where the predators can't get you. Some particularly large animals, like bison and buffalo, might evolve thicker, fire-resistant skin. All prey animals might have their eyes positioned differently so that they can look up without lifting their heads upwards, while still providing the horizontal range of vision needed to detect ground predators.
That said, your wyverns are not invincible; The hydrogen and chemicals needed to produce fire breath are precious and expensive to produce, so they can't breathe fire willy-nilly. Also, because they are flying animals, they will necessarily be lighter and less durable than a ground-based predator of the same size. Because of this, your wyverns will frequently be chased away from their kills by wolves, lions, or bears.
This has been a question weighing on me for a while, but I think that I have found an answer. If Wyverns are actually as big as they are depicted, 15 feet long and with a wingspan of 20 feet, it should have some problems dealing with its big body, and there would be one slight problem with that, a lot of animals would definitely view it as a threat, and maybe take opportunities to wipe the wyverns out in crews.
Although, the wyverns had a great potential to shoot fire, and that was an aptitude. So theoretically, if wyverns ever existed, I think that they would still be alive, and that they would be able to evolve, giving that they had a reasonable superiority to all other threats, except maybe other dragons themselves.
The last conjecture, and most of you will get a think about this, is that if wyverns had evolved, they would probably have wiped out the human race, because of their apparent intellectual superiority.
The threat post to wyverns can only be other draconic species or maybe a strong and intellectually advanced Dinosaur, but in the case that the only thing that existed were wyverns, they would certainly evolve.