How do I use my Apple ID balance to pay for stuff on the App Store

Balance is used automatically before charging any other payment method. There is nothing you need to do specifically.

Do note, that if your other payment method needs verification or has some other issue, it will ask you to verify it before the purchase can go through even if you have enough balance. Once its been verified it will use your account balance though before charging the other payment methods.

You cannot, there is no way around it. If it is requesting a payment method, you must add it and verify it.

As mentioned, once that is done, it will use your balance first before charging the other payment method, and you are free to remove it from your account after that.