I want to download games for my kids but it keeps asking for a payment

It is just asking for a valid payment method to be on file. You will not be charged to download free apps. If you have previous subscriptions that have not been paid for, then that will need to be done first.

If you can’t download or update apps - Apple Support

There are many ways to prevent your child from making purchases while playing a game:

• Use the Ask to Buy feature
• Parental Controls
• Require a Password for Purchases

You can review you account purchases using this link:

Subscriptions and Billing - Official Apple Support

You can also check at Settings > [name on top] > Media & Purchases > View Account.