$(a)$ What is the direction of magnetic field lines inside a bar magnet and outside of it?
$(b)$ What does the degree of closeness of the field lines represent?

(N/A) The direction of magnetic field lines outside a bar magnet is from the north pole to the south pole,while inside the magnet,it is from the south pole to the north pole.
$(b)$ The degree of closeness of magnetic field lines represents the strength of the magnetic field. The magnetic field is stronger in regions where the field lines are more crowded.