Today I have found an "IR Extender Cable" in my TV's paper box. (Exactly This Guy)
Am I able to control this thing, via my Jack Plug? I would like to write a script -if You guys can help me find a way-, to control my TV or whatever I want.
The fact that the interface happens to be a Jack is somewhat misleading. The Jack you see there is a mono jack but in reality is just a positive and negative hooked directly to an IR LED. The Internals of the TV are likely wiring female in series with the IR receiver circuit.
The fact that this uses the same plug as something that your computer also uses makes it a little misleading as the intended connection does not behave in the same way that a speaker jack would.
You may be able to control this from a Arduino or some other type of hardware where you are controlling the female end of the jack however. So that is a route you could pursue.