Can one who has lost a parent but is past the 11 months say kaddish d’rabanan after korbanos or any other time if no on else in shul is saying it? Is there any difference between saying kaddish d”rabanan or kaddish Yasom — with regards to this scenario?
Kaddish can be said, but there is a difference in that for Kaddish Yasom (the Kaddish after Aleinu) somebody should say the Kaddish, whereas for Kaddish De-Rabanan if nobody says Kaddish it need not be said (this is the ruling of the Rema, Siman 132; see also Mishnah Berurah 55:5).
The general custom is that somebody with both parents alive doesn’t say Kaddish, so that somebody who has lost a parent should say Kaddish after Aleinu so that the Kaddish is recited.
According to Kabbalah sources (in particular the Arizal and those who cite his rulings) the Kaddish De-Rabanan is also of great importance, and it can be recited too.