Apple ID: Changing and then deleting the old one. Will it delete downloaded items?

There is no reason to delete your Apple ID. Just change it, and you will lose nothing.

See the instructions below for changing an Apple ID.

Change your Apple ID  https://support.apple.com/en-us/HT202667Read these two sections very carefully to see what is allowed: If your Apple ID is a third-party email address and How to change your Apple ID if it ends with @icloud.com, @me.com, or @mac.com.

Before changing your Apple ID using a computer, sign out of all Apple services that use your Apple ID. If you are going to use an iPhone, iPad, or iPod, then stay signed in with your Apple ID on only that device. This instruction is taken from the above document under the heading Before you change your Apple ID.

For sign out purposes, see Where can I use my Apple ID? https://support.apple.com/en-us/HT202659 “This list is provided for informational purposes only and is subject to change without notice. It's not intended to include every feature or service that uses Apple ID. Visit the Apple ID support page for more information.”

And see What to do after you change your Apple ID or password 

 https://support.apple.com/en-us/HT204071

I would do this rather that delete it How to deactivate your Apple ID account  https://support.apple.com/en-us/HT208503

If you request account deactivation, you'll receive a unique alphanumeric access code. When you're ready to reactivate your Apple ID, contact Apple Support, provide your access code, and we’ll help you reactivate your account. If you lose this code, we won't be able to help reactivate your account." 

How to Delete your Apple ID Account https://support.apple.com/en-us/HT208504 

“While your request is being processed, you can contact Apple Support with the unique alphanumeric access code you received, and we’ll help you cancel your request. After your account is deleted, Apple can't cancel the request, reopen your account, or restore your data.”

_____________

And see How to create a new Apple ID https://support.apple.com/en-us/HT204316

Some of these things will apply to your situation even if you are not changing your Apple ID: What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071

You say: "For example, would the music downloaded on my iPhone be deleted? Would the deletion of my current Apple ID delete the things that are downloaded ONTO the device, or just the things affiliated with the iCloud storage?"

These things no longer will be available. You'd need to get them again.

I see no significant downside to just changing your Apple ID as I suggested above. Just ignore the old one.

It shouldn't delete them, but you won't be able to update any of the previously purchased apps, and you may lose access to some of your data.

It could be data from your apps. For example, if you have a Game Center account, if you delete the ID, you will no longer be able to access any previously played games.

If you delete the Apple ID, there will be nothing to share using family sharing

They might be able to access it, but they can't update anything because the shared ID has been deleted.

I delete the Apple ID

I am able to re-download the music, after my new Apple ID is added to the Family Sharing? Would that work?

If you delete the Apple ID, all content tied to it is gone. There is nothing to share.