Re: Genuine question about evolution
The idea of a species is, as you note, a matter of definition. If two populations of living things cannot interbreed, then by definition, they belong to different species. But reality is not so clear cut - there can be considerable variety even within a species. The scenario you present where an individual of an entirely new species suddeny appears (and cannot find a viable mate to continue the line) is very unlikely.
Speciation is a gradual process. Populations diverge over time, accumulating differences through mutation or selection until a point is crossed where they cannot interbreed any more due to those differences. Even then there can be a fuzzy borderline where organisms from divergent populations can, in principle, mate and conceive and produce offspring, though this offspring may be unviable, or unable to produce further offspring itself.