Ireland is the self-determination of the Irish people, it doesn't make it less democratic, but it still is a cultural product of Irish people. The same question regarding the United States is more complex, as it was a mix of immigrants from differents parts of Europe in the beginning, that rebelled against England, which I think can be seen as a self-determination for them, and in some ways an act of creation of a new peoplehood. But quite different from traditional peoplehood, because it's a peoplehood founded by new immigrants which have less in common, probably making it more volatile and/or open to change?
Therefore no to the first question, as these selfdeterminations are of other peoplehoods, and they aren't cultural products of the jewish people.
By homeland I refer to the land where the jewish people was born and is attached to, so yes I'm referring to Israel. Some zionists in the beginning were willing to forgo Israel and make a "temporary" state/autonomous region in some other place, in order to create a safe heaven for jews that were escapign persecutions (as this at the time was an impelling need), and that would politically fight for them at the geopolitical level. But forgoing Israel was never really accepted by the majority of the zionist movement, because it was the only place for which the jewish people would band togheter, and actually manage to self-determine.
I think that the way that the state of Israel was born was also (and not only) due to the Arab and Palestinian unwillingness to accept the jewish population, which in the beginning didn't even want a state. Actually the zionist current of Netanyauh comes from here and it's called Revisionist Zionism, it was a minority of the zionist movement. It was founded by Jabotinsky (not an admirable individual by many metrics, but some statments are worringly moderate if compared to Netanyauh), they wanted the creation of the state to be a main focus of zionism and for the state to be on both banks of Jordan, later expansionism became less of a focus. The idea of a state later did became more central to zionism because of growing tensions with the Arab populations and the inability of jewish and palestinian leaderships to find a way to coexist.