I know that according to the psak of the Shulchan Aruch the Sephardim (among others -- The Gra, many Kehillas in Yerushalayim including Chassidei Karlin, Chassidei Biyan I think, and Chassidei Chabad (in some cases when there is no shliach tzibbur making the bracha which I believe is their minhag)) don't make a bracha on Hallel (chetzi Hallel) that is said on Rosh Chodesh. While I don't have a specific reason to think otherwise, is the same true for the Hallel that is said on Chol HaMoed Pesach?
Yes, for Pesach Chol HaMoed, Sephardim recite the abridged version of Hallel and without any blessings. (cf. Yalkut Yosef 488:18)