The Rabbi says: "You shouldn’t say any of the morning Brahcot or Netilat Yadaim, just the Tikun Chatzot" But the Zohar, Vayakhel 14-25: “Rav Elazar and Rav Yossi were studying from the beginning of the night, when midnight came they heard the cry of the rooster and they did say the Morning Blessings.” How should I do?

Shalom, Even though there are various opinions on this issue, the simplest and most accepted one is as the Rabbi wrote - that is, if you have not yet slept at all, and it is now midnight, you should wait until the morning to say Birchot HaShachar. One may say the blessings from midnight, but there is an argument about saying the blessing on the rooster's crowing before daylight if one did not in fact hear a rooster - the Zohar you quote is talking about when the Rabbis heard a rooster. See the Shulchan Aruch, Orach Haim, 47, and the Mishna Brurah 31. Blessings.