This is an excellent question. Yes, in theory, it is possible to have a continuum, with no species at all. You see hints of that in, say, dogs, or some kinds of gulls. But let's consider the nature of adaptation here. Imagine a bunch of finches. Some have big, strong beaks that are good at opening nuts. read more
Regardless of how the barrier comes to be, once a barrier can separate a species into sub-populations, the machinery of speciation is set in motion. All species evolve over time in different ways, especially if their environment does not have a very long history of unusual stability. read more
If you have different numbers of chromosomes, or they are in a different order, it won't work. Within a species, the genetic codes are similar enough to be mixed with relative ease. Even then, not every combination works, or is without flaws; but there is enough similarity that getting a viable match isn't too hard. read more