Is it possible to overheat or damage the engine on an F-16?
Yes, you can overheat and damage an F100 or F110 engine just like any other jet engine.  It has mechanical and thermal limits that may not be exceeded.  And it often happens as part of high performance military flying, though it can make you very unpopular with your crew chiefs and inevitably with you commanding officers if you keep willfully exceeding the limits and damaging engines.

FADEC systems ie “power by wire” systems just use a computer to administer engine control commands based on pilot inputs.  They do not necessarily limit a flight crew from giving inputs that can exceed engine parameters.

Earlier engines were more finicky about this, in particular to exceeding hot section temperature limits or compressor stalls.  The F-14A with the TF-30 engines was particularly prone to compressor stalls and could be treacherous during critical phases of flight.  Improved intake diffuser, gas core aerodynamics, advancements in materials science and manufacturing plus improvements to fuel control units reduced the risks but did not eliminate them.