Well, strictly speaking, intonations are not necessary. Any question is just asking whether the whole proposition is true.
That is «Наш папа выступает по телевизору в пятницу» can be false because it's your friend's father who'll be on TV. Or because your relative will be on TV but he is not your father. Or maybe your father will be on TV, but not on friday, and so on.
The same is true for, say, english: “Will out father be on TV on friday?” can also be false in multiple ways.
The difference is that in Russian you use intotanion to stress that part ot the question you are particularly interrested in. If you know he'll be giving a speach on friday, but you are not sure whether he will be on TV or radio, you'll stress «по телевизору». If you are sure that your father will be on TV, but you're not sure when, you'll stress «в пятницу». In english you'll have to restructure your sentence: “Is it friday when our father will be on TV?”, while in Russian it is not necessary you just change your intonation. Although you can choose a different structure if you wish: «В пятницу ли наш папа выступает по телевизору?» and in this case intonation doesn't matter.
Update. And one more thing.
While you definitely can use intonations it might be a better idea to restructure your question and put the most relevant part closer to the end. It's not only easier for a non-russian speaker but it also sounds better.
- Мама, наш папа выступает по телевизору в пятницу?
- Мама, наш папа выступает в пятницу по телевизору?
- Мама, в пятницу по телевизору выступает наш папа?
- Мама, в пятницу по телевизору выступает наш папа?