are Buick century motors long lasting

Any engine properly maintained with frequent servicing, oil and filter changes and maintenance upkeep can last. However, there is no expectation or life expectancy published -- General Motors engines do not have the same reputation as a Honda or Toyota engine, to be sure, but again, when properly maintained, it has the best chance of longevity.

Yes - 300 k miles is not uncommon at all for the 3.8L - with somewhat regular maintenance.