Can I redownload a paid app?

In Android, once you pay for an app, you can put it on any device you own. I have some paid apps on all five of my Android devices. When you access the Play Store from the new device the app will indicate "PURCHASED" and you will be able to download it without paying again (provide, of course, you are still using the same Google account that you used to purchase the app.)

The same is true with iTunes.