Can new species appear or disappear in the biosphere?

Of course they can. This is exactly what evolution is aimed at – to weed out species that cannot adapt to environmental conditions, over time, more perfect individuals appear that can survive and give fertile offspring. This can happen both by natural selection and artificial, when a person intervenes. For example, the Amur tiger suffered precisely because of human hands, from natural selection we can isolate Archeopetrix or some kind of elephant turtles.