I cannot provide a full answer to all the questions you have here, but I can provide some context and some answers. Firstly, Arab-Jewish tensions had been growing steadily since the end of World War I. The Hashemites had long claimed control of much of the region, having claimed to descend directly from the Prophet himself. Thus, Jordan had envisioned taking complete control of much of the region. Jordan was also a colonial state in many ways, but the Hashemite family needed to bolster its claims to regional custodianship. Syria wanted at the very least to control the Golan, due to the strategic significance of the region.

My research on the matter has not focused on Saudi Arabia, Egypt or the other more distant Arab states, admittedly, so I can't comment on their designs. However I can say with confidence that Palestinian nationalism was not terribly strong- most saw themselves as Jordanian. This backs the Jordanian claim to the land at the time. In fact, some early partition plans included Jordan taking all of the mandate.

During the War of Israeli Independence (not using this as a partisan term), massacres of Jewish communities did occur, and the Arabs were particularly vicious in treating prisoners. It seems likely that the Jewish population would have been expelled or forced into refugee camps, though larger scale killing could've occurred. That said, it is difficult to support the claim that the Arab states envisioned industrial genocide.

As for the United States, there was a lot of disagreement in the Truman Administration. Military experts in the US did not predict a Jewish victory, and many cabinet members advised Truman NOT to recognize Israel because doing so would look particularly bad if the state was crushed by the Arabs quickly. During the war, the United States did not provide assistance to the IDF for this reason.

In summary: Jordan had the strongest claim on the land and likely would have wanted to annex it entirely. If not, Jordan would certainly have wanted control of Jerusalem. The US administration doubted the chances of Israel to win, and thus decided not to gamble.

If anybody has seen research that contradicts my work here, please let me know. I've done my best to gather information that is accurate, but I am not immune from mistakes! In addition, in the spirit of transparency, I should note my Jewish heritage as a potential source of bias, though I have done my utmost to make this completely non-partisan.

Sources:

Brilliant, Moshe, Micha Bar-ʻAm, and Sylvia R. Brilliant. Portrait of Israel. New York: American Heritage Press, 1970.

Cline, Eric H. Jerusalem Besieged: From Ancient Canaan to Modern Israel. Ann Arbor: University of Michigan Press, 2010.

Gilbert, Martin. Israel: A History. New York City, New York: William Morrow and Company.

Kollek, Teddy, and Moshe Pearlman. Jerusalem, Sacred City of Mankind: A History of Forty Centuries. Jerusalem: Steimatzky, 1991.

Naor, Mordecai. The Friday that Changed Destiny. Tel Aviv: Yehuda Dekel Library, 2015.

O'Malley, Padraig. Two-state delusion: Israel and Palestine - a tale of two narratives. New York: Penguin Books, 2016.

Followup question: Were there any plans or official statements/stances made by the Western nations who created Israel in the event of an Arab dismantlement (or even partial annexation) of the Jewish state they'd just created?