Can FMC be programmed to do fast maneuvering in fighter jets?
Pre-programmed high speed maneuvering is already being done in the case of target drones derived from fighter aircraft like the QF-16 (which is derived from F-16). According to multiple reports,


  The QF-16 ... is capable of pre-programmed maneuvers such as high-G turns, barrel rolls, split-S, etc.


While some research has been carried out on fully autonomous weapons systems, at present there is always a human being in the loop (at-least) for pressing the 'kill switch'. A few of the problems in a fully autonomous system operating in enemy airspace are:


Operating the UAV in hostile area and responding to threats. Though the QF-16 drones can fire chaff and flares to escape from incoming missiles, drones that can operate in hostile environment are still in their infancy. This requires significant improvements in ability of the UAVs to detect, differentiate and prioritize the threats and respond to them.
The UAVs should have the ability to search/track, acquire and engage the target while not ignoring friendlies or neutrals. Though some tests have been carried involving automated target tracking and some missile do have the ability to discriminate between the target and surrounding buildings (based on prior information),the technology is still some way off.
There are significant political, legal and ethical issues in using automated killing machines.


Some missiles like the Tomahawk has the ability to navigate along a predetermined path and hit targets, though they cannot do high speed maneuvers (or return, obviously).