So this can be used interchangeably with δημοφιλής?
Generally, yes. But note that δημοφιλής means not only famous, but also liked by the public (and that's the actual meaning of the world). So A.Hitler is διάσημος but definitely not δημοφιλής (by most people, I hope!)
As a 'shortcut' I'd add δημοφιλής = popular. ;)
Why isn't "Οι αδελφοί μου είναι διάσημοί" accepted for the audio exercise ? It has the very same pronunciation.