If I purchase an album (or song, book, etc) on the Apple Music app for Android, can I download it on iTunes for Windows?
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 subscription.