I'm wondering if there are any passages/prophecies about salvation for the Gentile world in the Old Testament. If you know any, please share.
YES, there are!
The footnote in my NLT Bible for Acts 11:1 has a list of Old Testament verses that say that salvation is for all people, not just the Jews. Below, I've reproduced the list and for two of them, I've directly quoted them because they're the clearest and most direct with regards to this topic.
Hebrew children in the Old Testament were born into God's covenant, both male and female. Circumcision was the sign of this covenant for boys, but the sign was not what saved them. Faith saved them. Rejecting the sign, circumcision, for boys, either by the parents or later as an adult himself, was a sign of a lack of true faith, and therefore the child was “cut off” from God's promises as clearly stated in Genesis chapter 17:
What was the purpose of this covenant with Abraham, Isaac, and Jacob? God tells us in the beginning of this chapter of Genesis:
This covenant wasn't just to establish a Jewish national identity or a promise of the inheritance of the land of Caanan, as some evangelicals want you to believe. In this covenant, God promises to be their God. Does God say here that he will be their God only if they make a “decision for God” when they are old enough to have the intelligence and maturity to decide for themselves? No! They are born into the covenant!
If Jewish children grew up trusting in God and lived by faith, they then received eternal life when they died. If when they grew up, they rejected God, turned their back on God, and lived a life of willful sin, when they died, they suffered eternal damnation. Salvation was theirs to LOSE. There is no record anywhere in the Bible that Jewish children were required to make a one time “decision for God” upon reaching an “Age of Accountability” in order to be saved.
Therefore Jewish infants who died, even before circumcision, were saved.
The same is true today. Christian children are born into the covenant. They are saved by faith. It is not the act of baptism that saves, it is faith. The refusal to be baptized is a sign of a lack of true faith and may result in the child being “cut off” from God's promise of eternal life, to suffer eternal damnation, as happened with the unfaithful Hebrew in the OT.
Christ said, “He that believes and is baptized will be saved, but he that does not believe will be damned.”
It is not the lack of baptism that damns, it is the lack of faith that damns.
The first promise to the Gentiles was given to Adam and Eve (Gen.3:15) who were not Jews. The second promise was given to Japheth, the son of Noah who was father to the Gentiles (Gen.9:27).Shem was the father of the Jews (Gen.9:26). This was later confirmed by Isaiah (Isa.54). And I might add two more things. The word Jew was given to Israel by the Gentiles after the Tribe of Judah. The Jewish people are actually of Syrian decent according to Scripture (Due.26:5). As for praying for Israel we should pray as we do for all men but asking God to bless Israel is a sin. Note (2 John 2:7-11). Only those that are in Christ are of Israel "seed" (Gal.3:16) and (Gal.3:27-29). Let Gods Word be true and every man a liar that does not agree with it. God bless those that are in Christ the Son of God.