Question: May a person act leniently when faced with a situation that is possibly, but not certainly, yichud? 

Short Answer: There are many poskim, including Rav Moshe Feinstein zt”l, who appear to allow one to act leniently when faced with a situation that is possibly, but not certainly yichud d’Rabbanan (Rabbinic).

Question: Should one comfort a mourner when he enters shul on Friday night?

 Short Answer: There is a custom for the minyan to comfort the mourner when he arrives in shul before the onset of Shabbos on Friday night. Some even allow such comforting on Shabbos itself.

Question: May an aveil attend his regular Daf Yomi shiur on Shabbos during shiv’ah? 

Short Answer: While the Aruch HaShulchan appears to allow an aveil to attend his regular shiurim on Shabbos, the minhag, as cited by many contemporary poskim, is that an aveil does not attend any shiurim on Shabbos during shiv’ah.