The Molli runs from Bad Doberan to Heiligendamm and Kühlungsborn, and vice versa. It does not run to/from Rostock main station (and afaik has never done so).
It never did. Rostock - Bad Doberan is a main line which was always normal gauge (1435 mm). While the Molli is a narrow gauge railway (900 mm).
After an longer interruption last year for track works it runs now again with normal frequency. In Summer more often than in Winter.