It is because rabbi is a respectful name meaning teacher.
Because it's an acronym for his full name: Ashkenazi Rabbi Itzhak.
A priest in Hebrew is "cohen". So people named Cohen are descended from Jewish priests. A Cohen / Kohen is specifically a Jewish Priest ascended from Aaron.
rashi's real name is shlomo yitzchaki
No, unless you are using it as part of a title like a story called "The Rabbi and the Bear", or in a persons name like Rabbi John Friedman.
The name of "teacher" is rabbi for Jews.
A practitioner of Judaism is called a Jew. A Jewish religious authority is called a rabbi.
You may address then as Rabbi, or just use their name; both are acceptable.
Rabbi Myers's birth name is Isadore Myers.
Shimona Rashi
There is no special word for the home of a Rabbi.
Rabbi Shergill's birth name is Gurpreet Singh Gill.