Why did Paul pray for the salvation of Israel if that is predetermined?
. . . my heart’s desire and prayer to God for Israel is that they may be saved. Romans 10:1
We don't know who the chosen elect are, correct? So, we are not assume it. Keep reading the run of the passages to get your answer. These brothers of Paul had a zeal for God but not according to knowledge. What knowledge is Paul referring to, here? The Gospel, to how a sinner is justified before a Holy God. Romans 10:
2 For I bear them witness that they have a zeal for God, but not according to knowledge.
3 For, being ignorant of the righteousness of God, and seeking to establish their own, they did not submit to God’s righteousness.
4 For Christ is the end of the law for righteousness to everyone who believes.
They don't believe that God imputes or accounts Christ's righteousness to sinners who believe God who justifies the ungodly by the righteousness of Christ, and not by trying to establish your own, which will never measure up, it's like us trying to touch the milky way with out hands. But these Jews believe they can seek to establish their own righteousness apart from Grace and they do not submit to God's righteousness!
Now, let's continue to the following verses:
5 For Moses writes about the righteousness that is based on the law, that the person who does the commandments shall live by them.
6 But the righteousness based on faith says,
“Do not say in your heart, ‘Who will ascend into heaven?’” (that is, to bring Christ down) 7 “or ‘Who will descend into the abyss?’” (that is, to bring Christ up from the dead).
This is why Paul prays for them to be saved, he doesn't know if they are the Elect or not.