>>>why would moshiach be someone who is alive? he will teach torah to moshe rabainu and the avos, who alive today is eligible for that?
I don’t understand this point.
You understand how Moshe will rise from the dead, and even how Moshiach will be someone who rose from the dead, yet you can’t comprehend Hashem giving a living person the wisdom to teach Moshe Rabbeinu?
Anyway, it’s clear in Torah that the תורתו של משיח will be divinely revealed to him, which explains how he will teach Torah to Moshe.
Sources:
1. The medrash says in ויקרא רבה (based on a posuk in Yeshaya) that a new Torah will come forth from Hashem in Yemos Hamoshiach, and in ילקוט שמעוני it explains that Hashem will give this Torah through Melech Hamoshiach.
2. The Rambam writes about Moshiach teaching Torah: בעל חכמה יהיה יתר משלמה ונביא גדול הוא קרוב למשה רבנו ולפיכך ילמד כל העם – Moshiach will be very wise and a great novi, and THEREFORE he will teach the nation.
This implies that Moshiach will teach Torah not just with his wisdom but also with the power of nevua.
(ראה קונטרס תורה חדשה מאתי תצא תנש”א)