1) who allowed Jews to migrate into british mandate before the creation of the state?

Jews lived in the area continuously for thousands of years before, so some Jews already lived in places like Jerusalem long before the mandate begun. Even modern Jewish immigration to Israel happened before the Mandate, which only begun in 1923.

The Brits tried to limit Jewish immigration into the territory of Israel. The Jews responded by organizing illegal immigration:

https://en.wikipedia.org/wiki/Aliyah_Bet

Though generally the Brits were pretty effective in blocking these efforts, as soon as they left in May 15th 1948, large waves of Jewish immigrants (especially refugees) flowed into the newly-established Israel.

2) since the british did not opposed jewish state, why did they allow it to form?

It wasn't really their choice. The Brits had a mandate in Israel for a specific purpose. They tried to follow an agenda that suited them, and did not include helping the Jewish minority establish their own country, but instead aligned them with the Arab majority in the region - with the obvious goal of gaining and maintaining influence in the region by this choice.

The Jews understood that very clearly, and launched an insurgency campaign to rid themselves of the hostile and indifferent Brits:

https://en.wikipedia.org/wiki/Jewish_insurgency_in_Mandatory...

This conflict soured relations between Israel and the UK for decades, arguably to this day.

The Jews accomplished their goal: the British mandate terminated and the Brits had to leave. However, the UK remained bitter towards the Jews and Israel, which reflected in its policy. The UK organized, armed, trained, and in some cases directly commanded Arab military forces that become major foes of Israel, notably the Arab Legion:

https://en.wikipedia.org/wiki/1948_Arab%E2%80%93Israeli_War

It also abstained in the crucial vote that legitimized the ultimate creation of Israel:

https://en.wikipedia.org/wiki/United_Nations_Partition_Plan_...

3) what's your take on the right to return?

The "right of return" is a unique invention with no historical precedent. Ethnic groups got into conflicts since the dawn of humanity, and frequently one would displace the other. Nations won territories from each other in armed conflict.

There was never a "right of return" in any of these cases. Refugees are resettled in available locations.

The refugees in this case are deeply hostile to the nation of Israel and in particular to its Jewish population. That's why they became refugees in the first place.

The idea to try to simply resettle them among the Jews they hate has no precedence in human history. In Israel's case, it will lead to the Jews becoming (again) a persecuted minority, and end their independence. There's no reason to assume an Arab majority will treat the Jews any better than they treated them before 1948 and the decades of conflict that followed - and they already tried to destroy them in 1948.

The Middle East is also not a place where minorities are treated very kindly in general. Neither ethnic minorities, nor religious minorities - and the Jews are both.

TL;DR the "right of return" is an invention by the "social justice" crowd to promote a policy that sounds just and reasonable but is without precedent in human history, and is designed to make the Jews of Israel into a persecuted minority, subject to the same violent attacks they've been suffering for centuries - while stripping them of the protection of having their own state and military force.