Re: Carriers??
Yes. But they tend to fly near to this floating airbase full of helicopters. And they tend to come at least in pairs, so there's someone with them who knows where they are to vector in the search-and-rescue boys.
Sea Harrier was also single engine.
I believe the US have been more picky about this in the past, until selecting the F35C. However this may be because modern engines are a lot more reliable.