The argument in the first question is an argument often framed as "Jordan Is Palestine". Raphael Israeli, a professor at Hebrew University, wrote an article arguing this point titled, "Is Jordan Palestine?", published here. His argument is that, in implementation, the Palestine Mandate initially included Transjordan, until it was severed by the British. This is something you can clearly see as having been the case in Article 25 of the British Mandate, which speaks of the area "between the Jordan and the eastern boundary of Palestine as ultimately determined" by the British. He also notes that until 1946, the British High Commissioner was responsible for both the remaining part of the Palestine Mandate, and Transjordan.

The question then becomes, why the split? Was it to sever the territory, one for Jews and one for Arabs? Or were there other reasons at play? In reality, the reason for the split was because the British saw that it was impractical and not desirable to argue that Transjordan should also be part of the establishment of a Jewish national home, and therefore severed it under Article 25 (which they negotiated) with this as a goal. The reason they didn't believe it was feasible was threefold: demographic (Jews would not likely constitute a majority in both portions of the area), political (Arabs would already have a strong objection to west of the Jordan River, but including Transjordan was even more), and historical (the British did not forget that the McMahon Correspondences promised the Arabs control east of the Jordan). The British adopted the position, according to Gideon Biger, that "Palestine is situated ‘west of the districts of Aleppo, Hamma, Homs and Damascus’", and that the McMahon Correspondences (and Sykes-Picot Agreement) made clear that Jordan was not to be a permanent part of Palestine for the purposes of the national home for the Jewish people. So in a way, there was acknowledgment that Jordan was intended to be the Arab state by the British, with Palestine as politically defined (for geographically, it was much broader) to be a Jewish national home. Their willingness to actually create a state in any sort of imminent way, and the strength of their convictions, is certainly up for debate. After all, it was only 1922 when Winston Churchill put out his White Paper stating that the "whole" of Palestine is not specified in the Mandate, and that a Jewish home only need be "in Palestine". Meaning, in short, not even all of Palestine need be "wholly Jewish". So there was a squishy sort of seriousness to the conviction by which the division was made between Arabs and Jews with Jordan and Palestine, respectively, given the British did not seriously seem to contemplate with conviction the hard split and decision to make the remainder of "Palestine", politically created as such, "wholly Jewish".

For the second question, that's a legal argument. We can note this much historically:

1. The argument typically made has been that the Mandate is not legally binding, but creates a territory that is not owned by a sovereign, and therefore is binding in the sense that its recognized rights of settlement still apply.

2. The Mandate was terminated by the Mandatory, and the United Nations assumed responsibility as was envisioned by the League of Nations, per Article 28.

3. The right to settlement is generally an argument couched in terms different from the Mandate. However, given the Mandate was terminated, it's hard to see how it could still constitute a guarantee of rights. Israel's legal advisors do not rely on the Mandate to justify settlement legality. The Levy Report summarized Israeli historical and legal arguments on settlement legality, and does not rely on the Mandate for legal support. Rather, it uses the Mandate and Balfour Declaration to note recognition of a right, which they argue can be derived inherently (not from a legal document) from the historical status of the Jewish people and the land. The Mandate recognizes a right that already exists, they argue, in the same way that the Declaration of Independence doesn't "grant" the right to life, but merely recognizes it.

I think it is hard to answer your second question as a result, because the historical and legal arguments made by those well acquainted with the issue do not line up with what you've asked.

I will note however that the White Papers constitute British policy, but none restrict the Jewish right to settlement in the land. While they restricted some areas in which Jews could settle, they effectively expired with the Mandate. The same is true of the Peel Commission Report, which contained nonbinding, never-implemented recommendations. Many of the White Paper policies were also never implemented. The UN Partition Plan was likely nonbinding and never-implemented. As a result, the argument is made that a right (which derives its legitimacy outside of legal documents) outweighs revoked or nonbinding policies.

For your third question, Jordan's annexation of EJ and WB was not recognized. The argument from the pro-Israeli perspective, made by law professors like Eugene Rostow in 1990, is that Jordan's annexation was not recognized, not legitimate, may have trampled on Israel's legitimate claim, and also was revoked and abandoned regardless in 1988.

I can't tell you the validity of these arguments, because I don't think it's good for historians to weigh in on legal arguments. I can only tell you what the arguments are. The counterarguments to each of these points are as follows.

1. The British intent for the split between Jordan and Palestine is irrelevant. It had no validity because it was colonial in nature and has no relevance today anyways, because the Mandate has been long since terminated.

2. The right of Jews to settlement doesn't derive based on history. There is no such right for any peoples to begin with, whether or not past documents long since terminated once recognized them.

3. The lack of a sovereign power does not mean Israel can settle the area. In reality, they still have to contend with the self-determination claims of the Palestinians and with the international community's opinion, as you yourself noted.

If you'd like to get into the legal weeds on these arguments, I suggest you check out the following, and try to draw conclusions of your own by conducting further research (this will only scratch the surface on both sides).

Pro-Israel Views:

• Eugene Rostow, "Correspondence", American Journal of International Law, Vol. 84, No. 3 (Jul. 1990).

• Eugene Kontorovich, "Unsettled: A Global Study of Settlements in Occupied Territories", The Journal of Legal Analysis, Volume 9, Issue 2, 1 December 2017.

• Abraham Bell and Eugene Kontorovich, "Palestine, Uti Possidetis Juris and the Borders of Israel", Arizona Law Review, Vol. 58 (2016)

Anti-Israel Views:

• Theodor Meron, "The West Bank and International Humanitarian Law on the Eve of the Fiftieth Anniversary of the Six-Day War", American Journal of International Law, Vol. 111, No. 2 (Apr. 2017)

• UNHRC Chanet Report, published in 2013

• W.T. Mallison Jr. and S.V. Mallison, "A Juridical Analysis of the Israeli Settlements in the Occupied Territories", The Palestine Yearbook of International Law, 1998-1999