Can I find out, who benefitted from an iTunes card?

If you decide to make someone a gift and send them an iTunes gift card you are not able to track who used up the amount on the card and for what specific app or else they used the money for. If you want to be sure that the iTunes gift card is only used by the intended person you can buy the gift card online and send it via e-mail. But you are unter no circumstances able to track the gift card after you gave it away

Apple has the information, but they will not provide you this. You have to involve the state attorney for a court order (Germany, Austria) best go to the next police station and asked them for help.

You‘ll get with every single purchase an invoice mail from Apple. The invoice always states who, in case of a iCloud Familiy used what time of currency f. e. ITunes benefit cards or a credit card to purchase a product. This is not limited to Apps or Music, it will show everything from in-app purchases to subscriptions. You may need to check you spam folder to. You can also go to the website https://reportaproblem.apple.com/ and check all you expenses there.