how to free up voicemail space?

Go to the Phone app, tap on the "Voicemail" tab on the bottom. You will see all the voicemails you have and then you can tap "edit" in the top right, tap the ones you wish to delete, and then tap "delete" on the bottom right once you are done.

Have you emptied your Deleted Messages folder? You'll find it at the bottom of the list of voice mails.

Question, if I tap “clear all” from the deleted message (voicemail) folder, will that just delete the messages in that folder or all messages on my iPhone? I need to save some of the voice messages.