>Now would it be possible for several, or even many sapient species to evolve on a single continent?
Well, it depends. When you look at our species and other human species, we eventually outcompeted ones like the Neanderthals in Europe.
However, if a species is limiting itself to a particular environment, then others species could survive unmolested in those spaces.
>Or just one per continent. and the rest of the species on said continent are only sentient like animals?
One per continent is probably a better idea, unless you can come up with reasonable way to keep some species away from each other.
>Were being bipedal, adaptability to different environments, and having no competition the only factors that guaranteed Humans could evolve higher intelligence?
It didn't guarantee it, but it certainly helped. Intelligence seemed to be built into our species, since it started springing up with each new human species that evolved, without being direct ancestors of us.
But there are many other factors that happened to result in our intelligence, just as it has resulted in intelligence with other animals.
>Also, I know we out-bred the Neanderthals, so would that situation be the most likely to occur on other continents where Humans never evolved?
It could do. Usually, the superior species will wipe out the inferior whenever they're introduced. But, again, if they have different strengths and weaknesses, they might survive.