Hi BravoSherpa,
We understand you have further questions about migrating to the Apple Music service. We're happy to further assist.
So it sounds like you had music files on your device prior to signing up for the Apple Music service. Then after changing over to the Apple Music service the items you already had show the cloud icon next to them. You'd also like to know why you have to re-download them. Those are all great questions we're happy to address.
When you use the Apple Music service, your library is loaded "to the cloud" this means that your library is all synced with iCloud so it is the same across all devices you use Apple Music on. When you set up the Apple Music service it will match items you have with the ones that are available in the catalog, and if an item is not available from the Apple Music catalog, it will be uploaded directly to your cloud library. As for downloading, you absolutely do not have to download them. They're available in your cloud library and you can just select the songs to start playing. If you would like to download items directly to your device so they are available to play when you do not have an internet connection, you can certainly tap the cloud icon to download them directly to your device.
Now for your second question/issue, it sounds like your library may still be syncing or in the process of migrating to the Apple Music streaming service. If you're getting an error that some of your devices aren't synced, we'd recommend making sure you have the "Sync Library" option enabled on all your devices. On iOS devices you can find this in Settings > Music. In Music or iTunes on a computer you can find this in Preferences > General tab.
Turn on Sync Library with Apple Music
Since you're new to the Apple Music streaming service, you can also find many helpful articles on how the service works here: Music Support
Thanks for contacting Apple Support Communities!