- I rule out this possibility: this is not grammatically incorrect, however people usually do not express themselves in this way. You may say, "I have ruled out the possibility of...", or "I decline this alternative..." or "I do not accept..."

-I rule out that she's passed: I rule out the possibility that she has passed (or, simply, "I do not think she passed..."

-After high school I ruled out the possibility to go at the university: After completing/graduating high school, I ruled out the option/possibility of going to university

- If you don't respect the rules you'll be rule out of the game: if you don't respect the rules, you shall be ruled out (or, "If you do not respect the rules, you shall be eliminated from the game)