Well I've never owned an Android device, but my parents have lots and I'm the one who has to fix it for them.
The way I add content to them is through Finder with drag and drop. Is there a better way? I'm not sure. This is the only way I know how to manage them.
About Google Music, that is Google's answer to iTunes Match. So yes, music needs to be uploaded for you to be able to access it via 3G/LTE, just like in iTunes Match. That's how I see it. And yes, I've also added raw MP3s to my parents phones through Finder, so there is that too. Is there a better way to manage Android phones? Again, I'm not sure, but this is how I do it.
About calendars, I'm pretty sure you need to use Google Calendars like you said. I don't think there is any other way to do it.