Can settlers/builders be captured at sea?
Is it possible to capture settlers, builders etc when they're embarked, or will they be killed?
Yes, you can capture them just the same as with land units, see screenshot:
You can not capture or even pass through a worker or settler at sea if your unit is an embarked unit. Maybe you can if you have the amphibious promotion but I havent tried. You can only do it with an actual naval unit. Frustrating when your scout is blocked by an embarked barbarian settler in a narrow straight and you can't pass by, let alone capture it.