When you download, you will receive the album as a .zip file which will usually unpack itself upon completion of downloading.
iPhones are designed to only work well with Apple Music/iTunes. But you CAN get your album into your Apple Music on your iPhone. Simply download the album to a computer that syncs with your iPhone, and you can drag the album into your phone from there.
If you download to your iPhone, the album will be found in your "Files" icon on your phone. There should be a "Downloads" folder in your Files that will contain the album. While Apple doesn't provide a way to transfer these tracks into your Apple Music, you can copy the tracks and paste them into a note in your "Notes" app. You can play them from there.