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Fasting and Hesped on the days before and after Purim:
Fasting:  It is allowed to fast before and after the days of Purim.
Hesped: It is permitted to give a eulogy on the days before and after Purim. [However it is questionable whether one may give a eulogy past midday of Erev Purim, unless he is a Torah scholar and the eulogy is taking place in the presence of his body.]
May one visit a cemetery on Erev Purim?
Tzidkascha on Shabbos Erev Purim:
If Erev Purim falls on Shabbos, Tzidkascha Tzedek is omitted from Mincha of Shabbos.
 Michaber 686/1
The novelty of this ruling is that it states in Megillas Taanis that all the holidays which are forbidden t fast on are likewise forbidden to fast directly before and after the holiday. Hence the novelty here is that since Megillas Taanis became nullified this law no longer applies. [Taz 686/1]
 Kaf Hachaim 686/2
 See Piskeiy Teshuvos 686/1; 696/4; Biur Halacha 547/3 “Shemutar”
 Gesher Hachaim 1 p. 259
 See Piskeiy Teshuvos 696 footnote 16 which explains the ruling of the M”A 696/5 to forbid going to a grave site on Erev Purim to only be referring to the women who lament over the grave, however the Avel may visit he grave at the end of Shiva.
 M”B 686/3