Can I download iTunes to my iPhone?

There is no app named "iTunes" on iPhones. There is an "iTunes Store" and "iTunes U" app and a "Music" app. If you want to purchase and download iTunes music, see: Buy music from the iTunes Store on your iPhone or iPad - Apple Support

No. The iTunes to which the article refers is an application for Windows and for old versions of macOS.

Your iPhone has a Music app for playing music, and an iTunes Store app for purchasing downloadable music from the ITunes Store.

No