how to download free apps without billing method or billing address

1.

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. 

As long as you only download free apps, it costs nothing.

Then your payment method remains intact.

If you are going to download a free app, there is a possibility to purchase the 'better' version, for example from a free version to pro version.

But that is not mandatory.

Use your Apple Account balance as default payment, then it is up to you whether you use it or not.

Free apps has also In-app pruchase.

Your payment method is actually a kind of deposit, if you buy something, it will be charged.

2.

If you don't have a credit card or don't want to use a credit card, you can also use your Apple Account balance as payment method.

See -> What you can buy with your Apple Gift Card or Apple Account balance

What you can buy with your Apple Gift Card or Apple Account balance – Apple Support (UK)

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• You can't use your Apple Account balance to send gifts or gift cards.
• If you use Family Sharing, your family members can't spend your Apple Account balance. Funds that you add to your Apple Account balance are only available to you. Find out more about how purchases are billed to your Apple Account balance.
• 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 also -> How to redeem your Apple Gift Card or App Store & iTunes gift card

How to redeem your Apple Gift Card or App Store & iTunes gift card – Apple Support (UK)

When redeeming a gift card, the amount will be credited to your (1) Apple Account balance and (2) you need to set your Apple Account balance as your default payment.

(1)

See -> Check your Apple Account balance > Check your Apple Account balance – Apple Support (UK)

(2)

See -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

If you already use your Apple Account balance, the Apple Gift Card or App Store & iTunes gift card is automatically added to your Apple Account balance.

If you update your payment method or add funds to your Apple Account balance, It would take about 1 to 3 business days in order to process.

If you're still unable to update your payment method, Contact Apple Support.

See also -> App Store & iTunes gift card -> Apple Gift Card - Apple (UK)

• Add money to your Apple Account balance anytime, no gift card needed.

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without billing address

You must provide your billing address.

Check / update your billing address:

Sign in to your Apple ID account page and edit / update your Apple ID details -> https://appleid.apple.com

• check / update your billing address.

or

(macOS) Set up your Apple ID payment method and shipping address on Mac

Set up your Apple ID payment method and shipping address on Mac – Apple Support (UK)

or 

Sign in to your Apple ID account page and edit / update your Apple ID details -> https://appleid.apple.com

• edit your billing addres.

or 

To change the billing address you can do (macOS & Windows OS) via iTunes

Start Music (-> Click on iTunes) -> side bar click iTunes Store -> go to Account (top bar) -> View Account -> Sign in -> Apple ID Summary -> Billing Address -> Edit.

or 

(iPhone & iPad) Go to -> Settings -> tap your Profile -> Payment and shipping -> Change Address.

Edit the Address -> tap Done. 

See also -> If you need to change or update your Apple ID payment method

If you need to change or update your Apple ID payment method - Apple Support

Click here for more support and assistance.