I think Singapore makes it easy to immigrate legally if you have a job offer (like Canada, Australia, HK, etc.). I don't think they allow for "family based" immigration.
That's basically correct, although the top tiers of the employment pass hierarchy are permitted to bring in dependents and parents. Only on long-term passes, though; becoming permanent residents, much less citizens, is off the agenda unless you're willing to sign up your offspring for at least two years of military service.
They have to leave Singapore before a fuzzily defined boundary between 10 and 12yo, meaning it's the parent who has to make the call. Stay beyond that, and they're a deserter who'll be arrested on sight if they ever return.