How do we know whether something was in our Qadr, predestined by Allah azzawajal, or whether our actions lead to a certain event? What things are definitely determined by Qadr that are unchangeable? And what predestined things can be changed by dua?
That is a complex question and there are many possible answers depending on what theory of qadar you believe in. Personally I like the views of al-Māturīdī and Ibn Taymiyya on qadar (as I discuss in this essay). According to that view, qadar is dynamic and changeable. God is always in charge of what happens to us, but God responds to our choices by changing our qadar. So if you do good deeds, God places good things and guidance in your path, and if you do bad deeds, God can place harmful things in your path. So it is all from God, but your choices affect what God decrees for you. According to this theory dua/supplication can change qadar.