Comparing the F-16 to Mig-29
What is the most important in the air fighter to be better ,the powerplant or speed?
and what is the most important the powerplant or range of the airfighter
and What is the most important too the service ceiling or powerplant ...
All this can be subjective. Range and speed are dependent on the thrust rating and specific fuel consumption of the engine(s).
I read in a recent magazine article that the F-16 and the Mig-29 in equally talented pilots are
equally maneuverable. However, the Mig-29 has large, thirsty turbofans compared to the F-16. With patience, the F-16 pilot can fight the Mig-29 to a dogfight draw
if the F-16 can stay away from the nose cannon of the Mig-29. The Russian fighter has less range than the American fighter, even though the Russian fighter is still quite maneuverable. The Mig-29 has a larger wing, and that adds fuel volume, even though the engines burn a lot of fuel in afterburner, potentially reducing its range as an interceptor. Peculiar mission requirements color the picture significantly as well.
Short answer: Too many variables for me to say.
... Generally What is the most important factor on the performance of the air fighter : the powerplant or the the speed or the range or the service ceiling? ...
Powerplant(s) thrust directly affect both speed and range.
Here's a ratio: 8 times the gas thrust horsepower should give twice the speed, but would require an immense engine. This shortens range. A lot.
I can look up the algebraic formula later; it's not with me now.
... and finally i want to know if the power/weight in an airfighter is higher than the other , does that mean that it is better?
It can accelerate faster, but with a possibly higher wing loading for a bigger engine, the resulting lower ceiling can limit this advantage.
Then there's and smaller fighter that inherently has a lower wing loading and higher ceiling, due to the inverse cube law, but has potentially less fuel volume to be able to take advantage of the larger opponent. An individually higher engine compression also means more relative thrust and potentially faster speeds. But, having a lower fuel/wt ratio mitigates this advantage as well.