In general, the Twilight Princess manga is regarded as canon. It adheres closely to the key elements and plotlines set in the original franchise. Minor deviations might exist for artistic or narrative purposes, but the core remains consistent.
They often interact as teacher and student. Luna, with her vast knowledge of the old magic, can teach Twilight things that are not found in modern magic books. For example, Luna might show Twilight how to communicate with the spirits of the night.
Well, the story behind the 'Twilight Music' in 'Twilight Princess' could be tied to the game's plot and the world of twilight. Maybe it plays a role in revealing secrets or triggering certain events.