My brother, passed away. When do we observe his first year Yartzeit? On the day of his passing or the day of his burial? Are there different rules for Ashkenazim and Sefaradim?

The Yahrtzeit is always held by the [Hebrew] date of death. If the burial was more than two days after death, there are some Ashkenazi opinions that hold the first Yahrtzeit only, on the burial day. [Pnei Baruch pp. 436-437] May Hashem comfort you.