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You can download free apps, but you may need to have a valid payment method on file, even if the app you want to download is free.
You can have a credit card / debit card on file and an Apple Account balance.
If you have set your Apple Account balance as your default payment method, your default payment method will be used first by Apple when you need to make a payment.
Free apps has also In-app pruchase.
See -> Buy additional app features with in-app purchases and subscriptions
Buy additional app features with in-app purchases and subscriptions
See also -> Apple Media Services Terms and Conditions
Legal - Apple Media Services - Apple
See also -> Payment methods you can use with your Apple ID
Payment methods you can use with your Apple ID – Apple Support (UK)
fyi: Not all credit & debit cards seem to work with App Store / iTunes Store, try a different one, or preferably a credit card. If your card is not accepted as a paymenf method, you need to contact your bank.