What is this big rectangular tab (?) thingy extending backwards just above the DC-10's #2 engine? What does it do?
(wikimedia.org, picture modified to point out the tab thingy)
It mostly houses the same stuff that's on an underwing engine pylon: bleed air ducts, wiring, fuel and hydraulic hoses and tubes that connect to the engine core and accessories. The aft part of the structure where it tapers is just there out of aerodynamic necessity.
Also the stuff at the end of the fuselage below the engine is just a fairing. It will fold away and the engine is removed by installing a bracket on the pylon and using cables to lower the engine straight down. If it was deeper in the fin as Sean mentioned, it would need to be drawn backwards and then down, making it more complex to do an engine swap.
DC10 rear engine pylon, same as underwing, for supporting the engine. The tube that looks like it could provide support is just a very long intake duct.