Are the days during Sivan when we do not say Tachanun also asur in Taanis?
Answer:
Yes. In principle, all days on which taanis is not recited are days on which it is forbidden to fast.
This applies even when a person has a yahrzeit, as the Chayei Adam (171:11) and the Kitzur Shulchan Aruch (221:7) rule. See also Mishnah Berurah 494:7, citing from Chok Yaakov (494:6).