Remember that the people replying to you here do not work for Apple. We are just customers like you and we can't do anything other than advise you as to the things you need to do yourself.
Can Apple review or cancel this unpaid charge if I did not intend to make the purchase?
You will have to ask Apple about that. The general pattern is to pay what you owe and then ask for a refund (which is not guaranteed). Report A Problem to ask for a refund; click here --> https://reportaproblem.apple.com/?s=6
Is there a way to restore my ability to download free apps without paying this disputed amount?
Again, ask Apple that. Don't be surprised if they tell you to do as in the previous section.
What should I do if Apple refuses to remove the charge?
Either pay what you owe and optionally ask for a refund, or you will be blocked from using the stores until you resolve this with Apple.
I suspect many issues arising from surprise charges are related to not understanding how charges for an item work. You always need to carefully read those. For example --> Cancel a subscription from Apple - Apple Support - "If you signed up for a free or discounted trial subscription and you don't want to renew it, cancel it at least 24 hours before the trial ends." This thread (particularly posts by Mac Jim ID) outlines complex scenarios regarding subscriptions and trials. ➔ Refund request for unintended Snapchat Pl… - Apple Community
This support page has information about contacting Apple support and service ➔ Contact Apple Support - Apple Support If live support options (chat and/or telephone) are available they will show near the bottom left.
- Telephone numbers may only work when calling from the same country.
- Chat options (telephone numbers appear as active links, not plain text) may depend upon cellular connectivity. If a number shows as an active link, click on it to see additional options.
- If chat is not available on the top level support page, try selecting your hardware and narrow down your issue to see if a support article offers a support link offering chat. For example, the contact support link on this page Check your Apple Account balance - Apple Support offers a chat link about emptying account balance even on a computer where the top level page does not offer any chat.