I’m being charged monthly for Apple Music. Can I download music onto my iPhone without the monthly subscription?

Apple Music is a subscription service and you can only listen to that music while you have an active subscription.

An alternative it to buy the music through iTunes. You do not need a subscription to do that. See: Buy music from the iTunes Store - Apple Support

If you decide to cancel your Apple Music subscription:

There is an Apple article that explains how to cancel subscriptions. Click on the following link: If you want to cancel a subscription from Apple - Apple Support

or use an internet browser to cancel as described in How to cancel Apple Music - Apple Support