It of course depends on the native aggression - generally I've found that natives with an aggression of 5 or more tend to rise up, capture the colony, and force me to send in troops at least once per province. So (unless their population is huge) I usually destroy them. The low agression ones (my favorites in this regard are Massachusetts and Kebec) can usually be kept on.
What happens is when your colony hits level 6, the natives join the population and make it a city, with population roughly 600 more than the native population. If you clear them, then the colonists work as we're all familiar with.
And yes - on shipyards, you only get one colonist per year for having shipyards. It doesn't matter how many you have. I usually end up with around 5-6 shipyards though, as I like to put one in each major ocean region I have bases in (North Atlantic, South Atlantic, Mediterranean, Indian Ocean, North Pacific, South Pacific, Indonesia - and often North Atlantic will have two, one in Europe and one in North America. I don't always have bases in all these regions though.) For instance, as France I'll usually have one in Kebec or Isle Royale, one in either Normandy or Morbihan, and one in Provence... and then build more as my colonies get more remote. In a recent colonial-Austria game I had them at Istria, the Falklands, San Bernardino and Timor.