OK Correction time:
1. Eretz Israel does not mean Greater Israel. Eretz is simply the Hebrew word for "Land". That is the Jewish name for what the Romans named Palaestina, a name that later came to be used by Christians (and not, as some would like us to believe, by Arabs). The Turkish name for that region while they held it, was Southern Syria. And among Israeli Arabs there still are those who consider themselves (and the Palestinian people) to be southern Syrians. The most prominent among those is Knesset Member Azmi Bishara, leader of the BALAD party, who has defied Israeli law several times by crossing the border to Lebanon and Syria and meeting with the leaders of those countries.
2. The question of the biblical and geographical borders of Eretz Israel is a difficult one. In any case it does not include the Golan Heights or Southern Lebanon, and probably not Ghaza as well. The territory of Jordan was actually included in the territory of the British Mandate in Palestine, and was cut off from it only in the 1940's. Until that point the territories along the eastern bank of the Jordan River were considered part of Palestine/Eretz Israel by both Jews and Christians (As mentioned before, Arabs considered this entire region to be a part of Syria).
3. Some of the quotes noted above are true (the Golda one for instance) some seem highly suspect (the Ben Gurion one), while others are completely false (cf. http://www.camera.org/index.asp?x_print=1&x_article=775&x_context=2 regarding the false Koenig quote). May I inquire where they were taken from (I mean where did the people to whom they are attributed actually say them)?
4. The term "Greater Israel", interestingly enough, is never used by Israelis. In fact, whenever you hear it you can be assured that the speaker is not Israeli. The term Israelis of the right wing would use is "Israel HaShlema", i.e. the "whole" or "complete" Israel.
5. In regard to what you name the most "reprehensible" deed, i.e. denying the existance of the Palestinians as a people, your charges are laughable and ignorant. Most of modern Arab nations are the result of British and French colonization. When Britain and France took over the Middle East from Turkey in the end of World War I, many of the national grouping we know today did not exist. Lebanon, for instance was carved out of the French mandate in Syria, because France wanted to create a Christian country in the Middle East. Jordan was created in a similar process, when Britain preferred to give the Hashemite Dynasty control over Transjordan. The majority of the Jordanian people, actually, claim to be Palestinians. This was not a practice that was unique to the Middle East. By the same process the French distinguished the Hutu from the Tutsi in Rwanda. Prior to the creation of the British Mandate in Palestine by the League of Nations, the term Palestine was almost unheard of in Moslem literature. This is what Golda Meir referred to in her (in)famous statement.
All that is not to say that the Palestinian are not a nation NOW. Since 1948 the West Bank of the Jordan River and the Ghaza Strip were occupied, first by Jordan and Egypt, and since 1976 by Israel, and over that time the people there, and their brethern within the borders of Israel have developed a genuine and real sense of peoplehood that has been ignored for many years by Israeli authorities (although it is now ignored only by the extreme right there). Just like the Lebanese they now identify themselves as a nation, and should be treated as such.