Are engines fed differently in reduced gravity aircraft?
Zero 'g' aircraft are basically commercial aircraft. 

In general, it is mainly the fluid systems like the fuel and hydraulic systems in the aircraft which are affected by the zero gravity conditions.

In the case of jet engines, the fuel is transferred by pumps operating under pressure and the fuel injection is also under pressure in the combustion chamber. Consequently, the engine fuel system does not need any modification. In a few aircraft, the fuel tanks themselves are pressurized (like C-5) but this is for safety and wouldn't affect operations.

The engine oil and lubrication system is also usually pressurized and can operate briefly under reduced gravity conditions.
Work done by NASA indicates that aircraft can be used in zero gravity conditions without any major modifications to systems.

The zero 'g' aircraft don't operate in weightless environment for more than 20-30 seconds and the engine systems should be able to cope during that time. The main concern appears to be the training levels of the pilot.