It means that you speak in the same language
The same language I speak in any location.
You speak the same language you spoke at the beginning of World War I.
No. Ancient Hebrew is a language, and Ancient Israel is nation.
For the same reason you speak English. That's their language. (However English is not your native language, I think)
Each person would speak the same language. Same can be said about any language.
Not necessarily. A language family can have dozens of different languages in it.
It is an interesting notion that religious groups "speak" a language. What language does Roman Catholicism speak? What language does Buddhism speak? Some languages are particularly associated with certain religious groups, particularly when the holy writings of the group are written in particular language, but there are quite a large number of Muslims, for example, who do not speak Arabic, or Jews who do not speak Hebrew.
it's the same way as any other language. How people speak English or Spanish or any other language..?
they do not speak the same because they are different tribes
It is their historic homeland. Ahad Ha'am explains that the Jewish Soul is intrinsically connected to his history and in the same way that a German-American can never be as properly German as a German in Germany, the People of Israel can never be as properly Jewish if they are not in the Land of Israel. The relics in that land speak to a Jewish sensibility and character.
Israel was declared an independent Jewish State on May 14, 1948. However, the phrasing of the question makes implicit assumptions that must be dealt with. It would seem from the way that the question is written that Palestine was a country and then one day, and was renamed Israel the next day. This is not the case. Palestine was a territorial name in the same way that the Riviera in southwestern Europe is a territorial name. It just happens that some of the Riviera is in France and some in Italy. Israel was a state that declared independence in that territory, which was a British Mandate at the time. There were still areas of Palestine that did not become part of Israel. Most of the Arab Palestinians did not consider Israel to be their state and would later identify with the Palestinian State declared in absentia in 1988 and recognized in the Oslo Accords of 1993.