Apple Music is a online library of music for a monthly subscription fee. As long as you setup your Windows iTunes to have Apple Music all music will available. If you add an album to your Apple Music Library, it will appear on all of your devices Apple Music Library as added.
I do not believe there is a way to "Purchase" music in Apple Music, it is a ...
Generally speaking, yes.
I imagine there is a minimum OS version on both Android and iOS but there is an officially supported (by Apple) method which they detail here. There is also an app "Move to iOS", that goes on the Android phone available in Google Play.