Should a detached EBS volume keep charging monthly?

You're always charged for EBS volumes because that data is occupying space on physical storage somewhere, even if it is not attached to a running instance.

In addition to the other answer, you can take a Snapshot of the volume, which stores the data in S3, a cheaper storage option. You can then restore the snapshot to an EBS volume in the future when you want to access the disk.

See Amazon EC2 terminology - AMI vs. EBS vs. Snapshot vs. Volume for more info on the specifics.

You can simply right-click the EBS volume in the AWS Web Console, and then click "Create Snapshot". After this snapshot is created, you can delete the EBS volume. Of course, I'd test restoring the snapshot and using the restored volume before deleting your EBS volume for good.

Should I delete the volume to avoid any charge? or there is any sort of stop or disable for volumes?

There is a delete on termination flag for the attached EBS volumes If this is set, when the instance is terminated the associated EBS volume is destroyed

You can set this flag when setting up a EC2 in the console or can use the aws ec2 modify-instance-attribute CLI command