The Boeing Aeromagazine article is a good one on the subject.
I think the answer is very situation specific. mr Boeing says if you take off you can land ( just check for contaminated conditions though ). So if all hell is breaking loose you should be able to get it back safely stopped on the runway . However you may well blow out some tires and risk a brake fire ( at very high weights). Remember on the 777 the landing distance given is for max manual braking , which on a very overweight aircraft equates to meltzone ( dammaged undercarriage at least)in most cases.
I think the various situations you ask about are case specific. If the engine just flamed out and the other was performing normally I would jettison if it was required to return. If it had a fire , severe dammage ( extinguished) I would need to evaluate the dammage and structural/systems integrity before deciding. eg if we had a "serious" fire that is now out . I would land ( as the wing could now have integrity issues). So there is no clear answer.
I feel the harder decision is the sick passenger example. You take off max take off weight. Just after take off , you are advised of a passenger who is gravely ill. Will you now go back and land ( blowing out tires , hot brakes etc) to save one life.?
This is a tough call , I would use all the resources avail to help mitigate my decision ( and back me up at the subsequent board). I would make pretty sure that I had the medical accountability given to the medical staff ( in my company Medilink). I would explain to them and the company the ramifications of an immediate return. If they felt the person required immediate help fullstop, then I would land. Its easier justifying the loss of a few tyres than the loss of life. But if they were wishy washy about the condition I would push then for tha wishy washy condition statement , that would protect me in court and delay while we get the weight down.
Off course if there is some other resaon that jeopardizes the safety of the aircraft I would not compromise all for one.
Good luck with the decision making , GREY GREY GREY