1.
You can download free apps, but you need to have a 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.
However, with the free version there is an advertisement.
Use your Apple ID 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 ID balance as payment method.
See -> 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 ID balance and (2) you need to set your Apple ID balance as your default payment.
(1)
See -> Check your Apple ID balance
Check your Apple ID 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 update your payment method or add funds to your Apple ID 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.