Your question answers itself.
(In Hebrew, we pronounce it Yisrael, but it's the same word.)
Israel.
Modern-day Israel is named after the ancient kingdom of Israel, which was named after Israel (an alternate name for Jacob son of Isaac son of Abraham).
A measure of weight and a name for coins in acient and modern israel.
Canaan
The State of Israel is a modern restoration of the ancient Jewish homeland. Jacob, the third the third patriarch, was given the name 'Israel' after his battle with an angel from God. The Jewish people are the Children of Jacob, otherwise known as the Children of Israel. Their homeland is the land of Israel. The official name in Hebrew is "Medinat Yisrael," the State of Israel in English.
In the Bible it was called Canaan. Today it is known as Israel - although modern-day Israel has somewhat less territory.
Israel became a lot more modern and city like.
They are in the same rough physical area and the descendants of Ancient Israel live in Modern Israel, returned after centuries of Exile.
The Negev Desert
Israel is part of the continent of Asia. The May 1948 Declaration that restored modern Israel named it "Medinat Yisrael" in Hebrew, or 'State/Region/Nation/Province of Israel', usually rendered in English as 'State'.
Yes. The Jewish State of Israel is a modern country with cars, computers, and all sorts of modern conveniences.
Yehuda is a city in Israel. Jerusalem is the capital city of Israel.