Yeshua is a variant on the name Jehoshua (Eng: Joshua). As such it was used by the people of Judea.

I believe that there was a 2nd century bce scribe called Yeshua Ben Sira. But I need to get a good source for that.

Many of the names in the new testament don't carry the connotations in Jewish populations that they do for Christian ones. Yehuda is a fairly common first name in Israel (I've known a few), but the English variant is synonymous with treason: Judas.

Yes to both. Jesus comes from Yeshua, which is a diminutive form of Yehoshua, ie. Joshua. "Jesus" and "Joshua" are really the same name in Hebrew/Aramaic and It was an extremely common name at the time. Josephus references 18 different guys named Jesus.

Christos is the Greek word for Messiah ("Anointed"). "Messiah" was a title of office for all Jewish kings and High Priests, so any High Priest named "Yeshua" was technically a "Jesus Christ" (it's like saying "Pope Jesus"). Josephus names four High Priests named Jesus. There is also a "Joshua the High Priest" (i.e. a "Jesus the Anointed") referenced in a vision in Zechcariah 3.

There is also one non-Jewish king who is directly called "Messiah" in the Hebrew Bible and Christos in the Greek Septuagint (Isaiah 45:1) and that is the Persian king Cyrus the Great who liberated the Jews from Babylon.