Can I use my Apple gift card as an iTunes card and how would I do that?

No. An Apple Store gift card can only be used in the Apple store to buy physical items. It cannot be used in the digital iTunes and app Stores.

If you want to change the type of card, you'll need to sell the Apple Care, and use the money to buy an iTunes gift card.

See here: What type of gift card do I have? - Apple Support