Hiii
As a PR u can work and stay anywhere you want in Canada. Dont worry about even if u re selected by quebec. Never mind. They dont care!!!!!!!!!!!1
Once you get PR, yes but for many of the PNP's, they require you to sign that you intend to settle in that province and if you apply for QSW, you are signing that you intend to live in Quebec so it would not be advisable for somebody who gets PR through those programs to go and land in a different province than the one that issued them the PR. So far I have not heard about the provincial governments going after anybody who decided not to settle there but that doesn't mean that they aren't or wont in the future.
There would not be much point for any province to have their own immigration programs if people can just land anywhere they want. I would advise anybody to go with what they signed to be their intentions for at least 6 months so they can not be accused of having lied on their applications.