Sea King Mk 3 and 3A have a Radius of Action (ROA) of 240nm when fully fuelled - that includes 30 mins on scene to effect the rescue and a 10% reserve.
The S61 has a different fuel tank layout and, when they were operating in UKSAR quoted between 190 and 205nm ROA.
The recovery depends on the size of vessel, the sea state and the time of day/night.
A vessel not underway usually sits cross-wind and cross-swell making it roll like a bastard.
In a big sea it is usually more comfortable for the boat to run down-sea which is often downwind and requires the helicopter to fly backwards in formation (not so difficult depending on wind strength).
Vessels under way, especially at speed, create their own apparent wind so it is often easier to operate parallel with the vessel or offset by 30-40 degrees to improve hover references.
The use of the hi-line usually depends on the size of the winching area available - into a yacht with lots of obstacles and a small cockpit, a hi-line would be best - onto a tanker with big open areas it's not neccessary.
Having said that, if it is a stretcher lift then we would normally use a hi-line for the deployment of the stretcher and the recovery of the casualty.