Is the Apple Music app for Android like the iTunes store? In other words, can I purchase movies, books, and audiobooks on the Apple Music app for Android? Or is the Apple Music app for Android just a portal to the paid streaming service?

Or is there another way to purchase movies, books, and audiobooks from the iTunes store using an Android device?
No, you can't buy apple movies, books etc except music. There is no way to do that via android device.But you can watch Apple TV on a smart tv.