1.
Check for sure the following Apple articles:
View your purchase history for the App Store, iTunes Store, and other Apple media services
View your purchase history for the App Store, iTunes Store, and other Apple media services - Apple Support
How apps, content, and subscriptions from Apple are billed
How apps, content, and subscriptions from Apple are billed - Apple Support
If you see "apple.com/bill" on your billing statement
If you see "apple.com/bill" on your billing statement – Apple Support (UK)
2.
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.
You can have a credit card / debit card on file and an Apple Account balance.
If you have set your Apple Account balance as your default payment method, your default payment method will be used first by Apple when you need to make a payment.
Free apps has also In-app pruchase.
See -> Buy additional app features with in-app purchases and subscriptions
Buy additional app features with in-app purchases and subscriptions
See also -> Apple Media Services Terms and Conditions
Legal - Apple Media Services - Apple