Why can't I download apps on my iPhone without it charging me on free apps

First see if you can regognize the charges, because is it not meant to be that you're charged for free apps. It can be that you'll need to provide a payment method before using the App Store, but this payment method will not be charged if you only download free apps.

1. To see your purchase history, go to reportaproblem.apple.com.
2. Sign in with your Apple ID.
3. A list of purchases appears. To see family members' purchases, select the Apple ID button and choose a family member.
4. To see the full receipt including tax, tap or click the date. Multiple purchases, including subscriptions, might be grouped onto one charge.

If the charge is for a subscription that you no longer want, you can cancel the subscription. Find out where else you can view your Purchase History.