A: Yes and no, children with DS aren't born with stubborn streaks any more than the rest of the population but children with DS are susceptible to more illnesses, learning and communication problems and these can lead to frustration and a tendency to 'act up' or present problematic/challenging behaviors.
Here are some links to some interesting articles on stubborn behaviour that I think are quite interesting and informative:
http://ndsccenter.org/
http://www.ndss.org/Resources/
http://www.down-syndrome.org/