Thank you for the details of the issue you are experiencing with playing music on your iPhone. In my experience, when songs are grayed out and the song won't play, the song did not completely transfer over to your iPhone and resyncing should resolve the issue.
If you are syncing automatically, resync content to the iPhone by unchecking "Sync Music" and click "Apply." Then check "Sync Music" and click "Apply" again. If you do not want to sync your entire library, be sure to select "Selected playlists, artists, albums, and genres" and select the content you want to sync:
If you sync manually, delete the music when your iPhone is selected in iTunes and drag new content to your iPhone.
You can find the syncing steps in the following article:
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