I am sitting shiva for my brother. May I learn every day my daily "Chitas"?
Answer:
To my knowledge the Chabad custom is to do so. In fact, Chabad read the Chitas even on Tisha Be'Av (though other authorities are stringent; see Shaar HaZion 554:11) - and the more so on days of regular Avelus.
Concerning Shnayim Mikra, the Aruch HaShulchan (YD 341:16) likewise permits reading Shnayim Mikra during Avelus.
Best wishes.
