Can I restore a app purchase that cost money?

Do you mean an in-app purchase, or do you mean an app you purchased?

07/2015 refund for game incorrectly purchased - https://discussions.apple.com/thread/7153649

iTunes Store: About In-App Purchases - http://support.apple.com/kb/ht4009

Yes. On your e-mail invoice there should be a link on it saying 'Report a Problem'

You will be taken to a website, where you will be asked for your Apple ID and password.

Select the purchase you want to refund.

and choose 'Cancel Purchase'

Hope It Helps!

AppleMan 🙂

<Edited by Host>