Are apps permitted to give monetary prizes? If an app has contests, is it a violation of policy to give payouts / money prices to winners of contests from the app?
Apple publishes general app review guidelines at https://developer.apple.com/app-store/review/guidelines/

Since payouts is money, then you have gambling issues to contend with and legal requirements to be sure each region is OK and you are licensed. Also, what sort of contest is being run. Poetry submissions or drawing - it really depends on what a payout and a contest is in practice. Then you are contracting and not just gambling.

Assuming contests are basically a lottery or game of chance, you would likely run afoul of a couple sections based on how you implemented the app:


1.3 Kids category, you cannot collect information from children, so no way to give "payouts" to them without violating the terms and/or COPPA / GDPR. 
3.1.2(a) Permissible uses - You get what you pay for. Make sure your app is valuable to all /equitable to all whether they win or not. (this ties closely with 4.2)
4.2 Minimum Functionality


  Your app should include features, content, and UI that elevate it beyond a repackaged website. 


This ties closely with 3.1.2(a)
5.3 Gaming, Gambling, and Lotteries


  Gambling, gaming, and lotteries can be tricky to manage and tend to be one of the most regulated offerings on the App Store.



You won't know until you submit the app for first review to test flight or app review unless you engage with developer support at a WWDC or support incident before you submit code. Also, consider those interactions will usually be - submit what you have and then we'll talk. Especially for section 5 Legal - you have to make sure you're OK before you hit up Apple for review.