Television on Saturday

Thank you very much
If it's reruns of old shows, or just a tape.
And if it's a place where you can't be seen, or alternatively it will spread in the public that television is like an air conditioner.
Will there still be a problem?

Reruns are also operated by a complete system of people. On tape, there is clearly no problem (essential. There is also a semblance of an eye).
And even if you cannot be seen, what is forbidden by a semblance of an eye is also forbidden in rooms.

If the prohibition is from the rabbis, I remember that it was added to the Mukhtar, and they wrote that there is no rule that applies even in private rooms.

Add the inscriptions of the s. a. d. ‘m.ma.achan’. And it does not seem so from most poskim.
See for example a nice review here:
https://www.etzion.org.il/he/%D7%99%D7%91-%D7%9E%D7%A8%D7%90%D7%99%D7%AA-%D7%A2%D7%99%D7%9F

And for the air conditioner to work at the electricity company, don't Jews work there?

Absolutely yes, but there is a need for a pico”n. What goes beyond that is a proliferation of classes, and it is not without problems. Of course, electricity on Shabbat is a much more essential need these days.

Does the fact that it is a vital need invalidate the halakha?

Does not eliminate, but allows for reliance on mitigating opinions and sufficiency.