Look for copyright and fair use in video games, it will lead you to everything you need to know legally speaking.
Basically, if it's intellectual property like a character, a song, a city concept, it's a big no no, you can't steal it, but the game mechanics and the story plot, no problem.
For the ownership, you don't need to do anything, copyright is an automatic process. You may want to protect the name of the game when the country is first-to-file regarding brands, but otherwise you only have to prove anteriority.