With whom? Israel has several very different and unique conflicts and describing them all would be very difficult. Perhaps the Related Question below on the Causes of the Arab-Israeli Conflict would help to answer a few questions.
This conflict, surprisingly enough, took place in what would become the territory of the State of Israel.
There is no such conflict. Abraham and his grandson Israel were never in conflict according to the Bible. There is also no conflict between the patriarch Abraham and the Modern State of Israel.
It is a desert in the southern portion of Israel.
this is a regional conflict
Zionism is certainly one of the causes of the Israeli-Palestinian Conflict. It is not the only cause of the conflict and is also not the most important cause of the conflict. Zionism is responsible for the existence of the State of Israel since Zionism was the Jewish Nationalist movement to establish a Jewish State in the Land of Israel. Without Israel, there would be no Arab-Israeli conflict. However, it is worth noting that while Zionism is a base cause of the Arab-Israeli conflict, numerous other far more lethal conflicts (like the Iran-Iraq War) have nothing to do with Israel.
Israel and Russia.
Israel controlled most of the Israeli conflict.
Israel.
Gaza
yes.
I am not quite sure what you mean by the Israeli conflict, since Israel is involved in numerous conflicts, both national and international. However, there is a high likelihood that the "Israeli conflict" is taking place in Israel.