"He appeared on TV" is correct.
"She didn't make it" is correct.
He appeared on TV, because he is not literally inside of the TV, he's on the screen.
She didn't make it, because of the "didn't" - that's why it's make. If you would've said "She made it" without the "didn't," you would use make
I checked your profile and I see that you're from Costa Rica, which means your native tongue is Spanish, correct? I happen to know a bit of Spanish, so I could help you a bit.
"In" means "inside." "On" means "on top of." Unfortunately, they're both "en" in Spanish, so there's no good way to translate it back. It's a similar situation with por and para for English speakers learning Spanish.
The second case is a little weird because you're using the present tense, but in the past. Just remember than whenever you're using "did," "didn't," "could," "couldn't," etc. with a verb, you would normally use the present tense, even when referring to the past or future.