If my Mother’s Great Grandfather was a Jew, does that mean I’m half Jew?

Well, first you to decide what you are meaning by Jewish. Bloodline, religiously, culturally, tribally...
You said above that you are now a Christain. So religously...you are not Jewish. (There are Jewish people who also believe in Jesus (Yeshua). They still follow food laws, and the feasts given in the Torah. ie. Jews for Jesus, Messianic Jews.
It does not sound like culturally you are Jewish. 
But bloodline you are 1/16th Jew.
If your Gr Gr Grandfather had married a Jewish woman on down the line continued to marry Jewish people yes you would be considered 100% Jewish. Or if you linage through the Gr Gr Grandparents stays on eaches Mothers side. (For the Jewish community to consider you a Jew)

I also read that Jewishness is passed on to the first born son. Is that nonsense?

And all of the other children of a Jewish mother.

I have never heard that.

I can’t find it now. Maybe I’m mistaken. I’ll keep looking