Does the modern SAR crew know how long the survivor has the potential to live before he/she is picked up?
no-one can know how long anyone else has to live
But yes, they often know the extent of the casualty's injuries, either because there is someone on scene already or because the person or passer by used their mobile phone to call for help.
The Whirly was used because we didn't have a choice - once the Wessex was available, the Whirlwind soon went out of service.
Perhaps not such a big a risk as you may think though since the biggest risk factor in accidents is the pilot, not the number of engines!
Except a single engine failure in a single is always dramatic - not so much in a twin. However you are right in this case - the inexperienced pilot couldn't hack it and could easily have clipped a blade or similar -the more experienced pilot chose to continue and ends up as hero or villan depending on his luck that day.