If I get to Kingsparrow Island with low chaos, can I go buckwild and kill everyone without ruining the ending

I believe all killing methods result in increased chaos. Since there are apparently non-lethal methods for disposing of your main targets, this might include them. Note that if you use non-lethal methods to dispose of guards and the like, rat swarms can still devour bodies and this might count towards increasing chaos (or missing achievements). There are "safe" places to dispose of bodies (like garbage containers). Elevated surfaces can also be safe, but if a body is not in a garbage bin there is a chance it will show up as "found" at the end of a mission (as near as I can tell). Generally I think sticking bodies on tables in isolated rooms is safe.

Also, see this PCGamer article. Highlights:

1. If you get a high chaos rating it can be brought down but it can take a few missions.

2. Bethesda says that if you maintain a <=20% kill ratio you should stay in low chaos.

3. Most creatures don't count towards the chaos total but Weepers do.

4. Re-wired trap kills and dumping unconscious bodies into water or dropping them from a great height count.

Violent solutions to problems and a high body count increase the level of Chaos in the city.

When the city is a violent chaotic place, people react accordingly. There are more guards and more traps. There are more rats to take advantage of the abundance of food. Essentially, if you signal to the game that a fight is what you're after, then a fight is what you'll get. The final mission, in particular, is dramatically altered by the level of chaos you've engendered or avoided up to that point.

Additionally, Dishonored has several endings, and chaos is the primary determinant of which of these you'll see.