Are there general rules on when the bow should go up or down? Should we always start on a down bow? And should we always end the tune with a up bow so when the tune starts again, it will be on a down bow. When should we slur? It seems to me when the note is short, slur should apply.
I don’t think there are general rules. Go up when up feels right and down when down feels right and slur when slurring feels right. That said, you can use bow direction and slurring to create accent patterns and rhythms which will dramatically affect the song you are playing. Look into the nashville and georgia shuffles for examples of that.