I'm not aware of an iTunes app for Android (and I do have an Android phone). If the icon you're referring to is Apple Music, that is the Apple subscription service. It is not suitable for your purposes, since you already own copies of the music that you want.
You cannot transfer music from an iPhone to another device (not even an Apple one) and as far as I know, the only practical way is to download your iTunes Store purchases to your computer, and then copy them to your Galaxy phone, using Windows File Manager.
Looking in the Android app store, I can see apps that offer to sync between iTunes and your phone, but I've not tried them have no idea how good they are.