Add Billing Method when trying to download a free app?!

Please try adding a different payment method. Most apps, even the free ones, offer paid upgrades, and in app purchases. Therefore, most require that you have a valid payment method attached to your Apple account before you can download the app.

If you would like to contact Support, follow the directions below.

1. Click on this link --> Choose your country or region - Official Apple Support  

2. Select your country

3. Select: Billing & Subscriptions

4. Select: Subscriptions & Purchases

5. Select: Update payment method

6. Select a chat session or a phone call.

Copied from iTunes support - Apple Community

It requires a valid payment method. That is true even for free apps where you would not be charged. The payment method needs to be from the same region as your device, which is how Apple determines if you are using the correct App Store. That prevents users from simply changing the region on their device to download apps, that would normally not be available in their current region.

If you can’t download or update apps on your iPhone or iPad - Apple Support

"You might need to have a valid payment method on file, even if the app that you want to download is free."

The payment methods you might use vary by region as outlined here:

Payment methods that you can use with your Apple Account - Apple Support