Psalm 2 celebrates the coronation of the king in Israel. It was to establish that the king was anointed by God for his God-given task. It warns the people not to rebel against God's king.

It is also prophetic. It is thought by many Jewish and Christian scholars to be a prophecy of the Messiah, and I agree that it is. But what it's teaching from that view is the God's Son is God's chosen Messiah. It's not making any statement about His origin, but only about His covenant relationship with YHWH.

So you think its not a prophecy, rather its speaking about kings here?

Jesus is eternal. John 1.1 teaches that Jesus was in the beginning with God, meaning that He had no beginning. Jesus's statement in John 8.58 also makes a claim to having been eternally existent.

As far as Psalm 2.7 is concerned, in the ancient world it was believed that the king (any given king) was adopted by the god to be his seed, making the king semi-divine. It's not speaking about physical birth but more so about this king being a representative of god on Earth.
Kings in David's line also held their kingship by divine adoption, a view that was celebrated on the coronation day. This "adoption" metaphor was rooted in the covenant relationship between YHWH and the David kings. In seeing this text about the coming messiah (Jesus), then, it's a claim that the messiah would be God's representative on Earth, rooted in the covenant relationship between Him and God (and therefore also the people and God). It doesn't really speak to the issue of whether or not Jesus is eternal.

I know Jesus claimed to be God according to the gospel accounts, and several Pauline epistles etc… but was Jesus created by the Father? Or is he eternally existent?

Psalm 2.7 seems to indicate he had a beginning.