The bracha on putting on a Tallit uses the word "lehitateph", meaning to enwrap. What is the source of this wording? More than that, the Kitzur Shulchan Aruch says to wrap the whole tallit around the head before making the bracha and only then lowering it back to cover the body. Is this an essential part of the mitzvah?

ב"ה Shalom and Moadim Le'simcha The source of the wording "lehitateph b' Tzitzit , is from Talmudic sources , from the Tosefta Berachot Chapter 6:15 . the Talmud Menachot 43a also tells of Rav Yehuda who would say the blessing ""lehitateph b' Tzitzit" every morning. This is codified in the Shulchan Aruch 8:1, and then copied in the Kitzur Shulchan Aruch. Wrapping the Tallit around the head is brought in the Mishna b'rura and this is the accepted and common practice. All the best