Is aveilus a din or halacha?
Answer:
This depends on which aspects of aveilus.
Some of the practices of aveilus are matters of custom that were enacted as rabbinic obligation. This includes for instance tearing one’s clothes.
Some are customs that do not involve a full rabbinic enactment, but are still obligatory by force of the custom. This includes the idea of 12 months of aveilus for a parent.
The basic concept of aveilus could be Torah law; authorities dispute whether the first day of aveilus is a Torah mandated law or rabbinic enactment.
For details on this I would recommend reading through the Aruch HaShulchan (Yoreh De’ah 339 and on).
Best wishes.
