One should not take off his Tallit until after Alenu L’Shabeah (Torah Lishmah 148 by the Ben Ish Hai, Rav Yosef Haim of Baghdad, 1833-1909). According to the Arizal, as brought in Sha’areh Kavanot, there is a mystical connection between Alenu and wearing a Tallit.
One should remove the Tallit while standing, just as he put it on. (Kaf HaHaim 24:9, Rav Yaakob Haim Sofer, Baghdad-Israel, 1870-1939)
Of course, one should first remove the Tefilin, before removing the Tallit. Just as he put on the Tallit first without Tefilin, he should remain with it last, without Tefilin.
One should remove the Tallit with his left hand, the weaker hand, in order to show that it’s difficult for him to leave this Mitzva (Ben Ish Hai, Parashat Noach 16).
Everybody should fold his own Tallit, as opposed to giving it to someone else to do so, which is bad for his Mazal (Ben Ish Hai).
One should not leave his Tallit unfolded overnight. If he did, he should shake it out before donning it in the morning, in order to release the negative energies that attached themselves to it during the night (Ben Ish Hai).
One should not fold his Tallit during Kaddish, especially while answering Amen Yeheh Sh’meh Rabah. Kaddish is no less than any other Beracha, in which it is prohibited to engage in any other activity. However, Hacham Ovadia holds that once the first half of the Kaddish has been recited, it is permitted to fold the Tallit.
Once the Tallit has been folded, it is proper to kiss the four tassels of Sisit, before putting it in its bag (Ben Ish Hai, Bereshit).
