A very compledx question where one aqnswer does not fit all.
My suggestion is to parse this down to one question at a time if you really want to cover all possibilities.
In general, as long as there is a means to limit the source of fuel (spar valves etc.) then prioritize that action and protect the critical aircraft parts from excessive heat. That should keep the fire from spreading beyond the engine.
Damage cost is not an issue here but spread could affect cabin safey and or threaten fuel tanks. If you can stabilize that threat than you have lot's of time to try what you please with the engine.
Generally most engine fires will expend their source of fuel within minutes (petrol and oil) so ifr you protect the aircraft f9or that time period you have greatly reduced the safety risk.
Historically the most difficult engine fires are those where the spar valve can not be shut off starving the fire or the fire has progressed beyond the heat shield into the pylon.
Fires which are inpervious to shutting the spar valve are those where oil metal, or combustible internal materal is involved.
examples are : compressor titanium fires, magnesium accessories, or composite reverser cascades, In these cases the fuel is typically used up in minutes even though you are very unlikely to be able knock it down in that period of time.
As for shutting down running engines without shutting off the fuel I've seen blankets and/or lots of water work sometimes. But you may have lots of time to work on this as long as nobody goes near it. (The World Airways DC10 in Boston harbor comes to mind). If you are going to use water, try and aim an intense solid coulumn just outboard of the center body/spinner. That's the only way you can get it into the core (fan engines are designed to shed 90% of water spray out the fan ducts)
Ok that's enough for the time being to start the thread discourse