This is one of the more sane posts I've seen here. Chinese can develop the technology, the problem is they don't have it right now. Same with the Indians, they can develop the technology, but the fine-tuning aspects of building a fighter jet engine don't just come overnight.
You have to gain knowledge either through an iterative process (trial and error like the Chinese), or have someone come in and teach you how to build it (India and Snecma).
Both methods will work, but right now neither country can mass produce reliable engines.
A turbine engine, in principle, is an internal combustion engine, like the one powering your car. You have an explosion contained inside a chamber and you channels the force into mechanical contraptions to produce work.
The great difference here is that with a piston system, the one in your car, temperature peaks and mechanical stresses are never constant so 'regular' metals like iron/steel or aluminum are well able to handle the temperature and mechanical stresses. Not so with a turbine engine where temperature peaks and mechanical stresses can be constant, as in combat. Not only that, any temperature and mechanical stress levels below peaks will also be constant, as in an airliner cruising.
The internal combustion temperature of the F135 engine is top secret, but you can bet your next year's salary that it is in the four figure range and anything in the public realm is pure speculation.
http://www.uwplatt.edu/~schlager/web pages/ME turbines.html
The F135 gas turbine is the first production jet engine in this new 3,600°F class, designed to withstand these highest, record-breaking turbine inlet temperatures.
High performance combat aircrafts cannot, or rather should not, be designed for a wide variations in engine performance. Their ability to maneuver, as in roll or climb rates, are just as dependent upon engine capability as their aerodynamics designs. Fly-by-wire flight control systems (FBW-FLCS) can make accommodations via widening the flight control laws parameters (software) but even those laws are restrained by physical limits of the flight control surfaces and their mechanics, wing area and shaping, center of gravity, etc...So either a design have matching engine, or the design be scrapped.
This is why engine design and manufacturing are so critical and can make or break a fighter.
