I know I cannot make a profit from a game based on a movie or a TV-Show without permission, and licenses, and all that stuff.
But if I make one, can I apply it and publish it completely for FREE on Steam and other platforms without being rejected?
If the movie or TV-Show is Japanese, you possibly can. You could even sell your game, possibly. In Japan, there's an entire industry built around fan-made derivative works. Comiket is an event specifically created for people to sell and buy such things, and it attracts over 600,000 fans per year. There are also online shops and brick-and-mortar stores that sell doujinshi all year round.
In Japan, it's basically considered legal until the IP holder files a complaint, and most of them don't. Some publishers even explicitly/officially allow it, provided that certain guidelines are followed. But there are definite exceptions. For example, Nintendo will come after you pretty fast if you try to make a Pokemon game.
Kinda just depends on what you wanna do, and how you wanna do it. I doubt you could publish a doujin game on Steam, but there are places where you could publish it (such as DLsite).
But if you're wanting to make a game based on an US intellectual property, then you're pretty much out of luck.