Apple charging for youtube premium Account

Apple won’t just randomly charge you for things. You or someone with access to your account must initiate the subscription for Apple to charge you. But yes, Apple can charge you for Youtube Premium if you started the subscription through the App on an Apple device.

You can view your subscriptions and cancel them if necessary by following the steps here: link-> If you want to cancel a subscription from Apple - Apple Support

No, you should not need to open an account to cancel anything, that fact you are being charged means you already have an account. Not sure, what you saw with Apple Music, but you need an account first before you can be subscribed to anything.

Please follow the steps in the support document I linked to above to cancel the subscription. Here it is again: link-> If you want to cancel a subscription from Apple - Apple Support