What is the point of 'sync music' in iTunes if I have to click 'make available offline'?
I hope you only use iTunes purchases not Apple music.
So the answer for your first problem is,
that If you sync them, they will be available on all of your devices. However, making them available offline means that you can listen to your music wherever you go. You do not have to be connected to WiFi. So sync only add them to your Music app automatically. Point is that some people don't have enough space to download every song since their library is like 20GB. So they use Wi-Fi to download their song when they needed.
Answer for second question :
So as far as I know , they now use iCloud to sync all of your music to your every device through iCloud. So whenever you purchase some music it will automatically being available on your iPhone. Then you have select download if you wanna listen offline.
If you like to make them automatically download to your phone without touching download for every single song, just goto Settings -&gt; Music -&gt; Under downloads turn on &quot;Automatic Downloads&quot; . That would automatically download your songs.
Since you have DRM enabled songs on your device ( Purchased from Apple) you cannot simply do whatever you want. If you want to play with them as before they use iCloud, you have to manually download that song from internet and add them to iTunes. Then sync to your iPhone. Otherwise as Apple Supportive person told me there will be no option because, you run out of space.
If you don't like to manually do what I said, you have to do keep itunes purchases only synced. But that will not solve your problem. If this ain't clear enough just add a comment. Thanks.