How to create child iTunes account without credit card

If your child is younger than 13, they're not allowed to have an iTunes account, unless you create one through Family Sharing:

Family Sharing and Apple IDs for kids - Apple Support

If your child is older than 13 and you want them to have an account without credit card options:

Create an iTunes Store, App Store, or iBooks Store account without a credit card or other payment method - Apple Suppor…

If you want your child to have your iTunes account on their iOS-device but not be able to buy anything, you can use parental controls to restrict your child:

iOS: Understanding Restrictions (parental controls) - Apple Support

No, from Family Sharing and Apple IDs for kids :

Before you begin, make sure that you're using a credit card as your iTunes Store and App Store payment method. To comply with child online privacy protection laws, you will use the CVV or security code from a valid credit card as part of providing your parental consent. If the card on file is a debit card or another payment method, you’ll be asked to provide a credit card before you can continue. After you create the child's Apple ID, you can change your payment method back to a debit card.