Note-The following is an attempt to answer the OP. It should in no way be read as a declaration that my religious beliefs are superior, or that I believe Judaism has a monopoly on truth, righteousness, or Baltic avenue.
The messiah is supposed to be a descendant of King David. Such descent would be traced through the father and would not be passed on to an adpoted son or stepchild. If Jesus had no human father, he cannot be David’s descendant.
The messiah is supposed to gather all the Jews to the Promised Land. Scuba Ben and I live in Philadelphia. Zev Steinhardt and CmKeller live in New York. When visiting my parents in Florida, I’m surrounded by Jews.
The messiah is supposed to bring peace to the world. If that happened, I missed it.
For more, Rabbi Joseph Telushkin’s Jewish Literacy has a section on the messiah.
You can read it here
Finally, the Jewish messiah has to do all this in one life. Judaism explicitly teaches that there is no Second Coming provision. Zev could be the messiah. But, if he dies without gathering all Jews to the Promised Land, ushering in world peace, and doing a few other required things, we’ll know he wasn’t. Many members of a Lubavitcher sect thought their leader rabbi Shmeerson could be the messiah. Then, he died. While still revering him as a great hero, all but a tiny fringe of the Lubavitcher accepted that Shmeerson wasn’t the messiah.
Re Nazarite
When you feel the need to atone for something, to feel closer to G-d, or because you feel like it, a Jew can make a pledge to G-d and become a Nazarite. This means- no alcohol, no sex, and no cutting your hair. On Yom Kippur, the day of atonement, Nazarites say a special prayer asking G-d to forgive them for not fully partaking in the world He created.
Re Almah
For once, I don’t have to defer to Diogenes’ authority. I’ve asked rabbis, teachers, and folks who speak fluent Hebrew about this. Diogenes has summed up their answer. Almah is better translated into English as “maiden”. It can be to imply virgin or unwed, but the dictionary meaning is “girl”.