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.
Free apps has also In-app pruchase.
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.
Some purchases might require you to have a credit card on file, even if you use your Apple Account balance to make the purchase.
See -> If you can’t download or update apps on your iPhone or iPad
If you can’t download or update apps on your iPhone or iPad – Apple Support (UK)
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Add a payment method
You may need to have a valid payment method on file, even if the app you want to download is free.
Add a payment method
See also the following Apple articles:
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.
Remove a payment method from your Apple ID
Remove a payment method from your Apple ID - Apple Support
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If you can't remove a payment method
If you have subscriptions like iCloud+, have an unpaid balance, or you use purchase sharing, you must keep at least one payment method on file.
If you still need help, get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service or check -> here for more support and assistance.