Unfortunately that quiz is a load of tosh (would love to use a stronger word but feel AB will censor it.) I shall explain:
True dog breeds, e.g. labrador, poodle, malamute, bichon frise, will always breed true, i.e two labradors crossed will produce a labrador. That includes a labrador's temperament and behaviour and well as physical size and appearance. You have an idea of how that dog will act.
The new 'designer breeds' aren't real breeds and will not breed true. Labradoodle x labradoodle does not give a labradoodle. When you cross two breeds you have no idea what you're going to end up with, both in temperament and appearance. You might get the best of both breeds, or you might get the worst. Usually you end up with a mix.
Schnoodles are usually no more hypoallergenic than the next dog. Only some poodle lines can be considered hypoallergenic, and the only way of finding out if a dog is hypoallergenic is by testing reactivitis and such. A schnoodle, poodle or any poodle cross in a shelter, and most from breeders, will likely not be hypoallergenic.
And as for living with a new family, that depends on the dog and its training, not on the breed.