is using apps that give you itunes money allowed? such as app nana?

It's not a matter of being "allowed" or not, since as long as they're not apps in the iTunes Store Apple has little or nothing to do with such promitions, but what sort of risk you want to take. Many of these sort of promotions don't pay off much if at all but just get you onto numerous mailing lists and entice you to do the same to your friends and relatives. Some such "promotions" are out and out scams designed only to get your personal information. So examine any such program carefully and understand that even the best of them may not be worth all the emails and perhaps physical mailings you'll get or all the hoops you need to jump through.

Regards.