Human evolution: Where *exactly* did the first human come from, whose parents were not?
but I get lost on the 'border' cases.


Not surprisingly, since there are no borders, and this is probably the greatest misunderstanding: Evolution is gradual. It’s not generally possible to say where a complex feature (or a species) starts and another one ends. We could in theory say, for individual mutations on the genetic level, in which generation they first occurred, or when they became fixed in the population. But we cannot infer from these atomic changes where our ancestors started becoming humans. So the whole concept of “first human” is not biologically meaningful.

The best analogy remains a gradient between two colours. Going from the left, where does blue end and red start?



By the way, you spotted this very well by yourself:


  [if there is no first human] then that necessarily means that the definition of a species is itself fuzzy


Exactly, that’s the case. For more details on definitions of species, refer to MCM’s answer. But it’s indeed crucial to note that the definition of species (or any other biological classification) is an ever-changing approximation which tries to fit a definitive yes/no answer onto a gradually changing scale.