1) One must concentrate when answering the Kaddish. Chazal said that whoever answers Aman Yehei etc. with all his strength will have his sentence torn up. The explanation of “all his strength” is both with all his concentration and with all of his limbs, so that he says it with heart and soul, and not just like someone who says it with his lips but his heart is not with him. (Shulchan Aruch 56)
2) One must be very very careful not to speak during Kaddish and Kedushah, as Chazal tell us about Rebbi Chama who saw many thousands of camels loaded with anger and rage to punish those who speak at those times. About anyone who speaks at these times, the verse says “And not I did you call Ya’akov!”. Even thinking about words of Torah is forbidden when listening to Kaddish. (ibid)
