How to transfer iTunes files to Chromebook on iOS?

Anything in the iPhone can be transferred.

You can look for third party apps that may work on a chromebook to extract the music from the iPhone. Not sure. If there are any though.

Alternatively you can use iExplorer on a Mac or Windows PC to extract all the music from the iPhone: https://macroplant.com/iexplorer

Not possible. There is no version of iTunes for ChromeOS, Sorry.

You need a Mac or Windows PC.

Unfortunately, to transfer music data from your phone to an external hard drive, you'll need a PC or Mac with iTunes.