1. Question: If a bar mitzvah boy who turned 13 Friday night did not develop 2 hairs until Shabbos morning is still obligated to say the night time kiddush during the day then why is an onen, someone who is waiting to bury his dead relative, in this case over Shabbos, exempt from saying havdala after the burial on Sunday according to the Rosh?
A: The Minchas Chinuch (mitzvah 31) says that if the bar mitzvah boy could not say Kiddush for himself on the Shabbos night he is obligated according to the Torah to say kiddush on Shabbos day because the kiddush during the day would not make up for what was skipped rather there is just a Torah level mitzvah to say the night time kiddush at some point during the whole entire Shabbos. (The daytime kiddush we say is rabbinic.)
B. The Rosh brought in the Tur Yoreh Deah 341 says that since an onen was not obligated to do havdala on motzei Shabbos at the beginning of his obligation to say havdala then he is exempt from saying havdala the next day after the burial, for since he was not obligated by the main time of obligation he is not obligated anymore (though havdala technically could be said until Tuesday normally.)
C. The obligation of kiddush comes because of the concept of Shabbos but the obligation of havdala comes because of the separation between Shabbos and weekday.
Answer: The obligation of kiddush is because of the day and the whole day is Shabbos so the bar mitzvah boy is still obligated once he produces his two hairs. But the obligation of havdala is the separation between Shabbos and weekday which is really a moment in time, once it passes and the onen was exempt at the time then he is not obligated any more or get a renewed obligation once he buries his relative. [/exapnd]