Offline songs are available from 4.0+ version! Anyways, to fully enjoy the app indeed, is required to be connected to WIFI or Mobile data + to be subscribed to Spotify and Morning.
PS: Soon we will incorporate Music Library as a source which means that you will be able to use your songs saved there in offline mode! Wait for it 😎
You can still keep Do Not Disturb activated both online or offline, the alarm will not be affected by this.