Your prayer reflects a sincere grief over sin and a genuine desire to see people come to know the truth that is found only in Jesus Christ, and that is a burden God himself places on a heart that cares for others.
You quoted Psalm 51 rightly, that God does not delight in outward religious acts alone but in a broken and contrite heart. That is the work only God can do. We can pray for people and speak truth to them, but we cannot create that brokenness ourselves. The Holy Spirit must open the eyes and soften the heart so that a person sees sin as God sees it, hates it, and turns from it. Your request that God would stir their hearts and give them a thirst for truth and righteousness is exactly in line with what Jesus promised when he said blessed are those who hunger and thirst for righteousness, for they shall be filled.
Scripture reminds us that deep inside every person there is a thirst that is ultimately a thirst for God. People try to satisfy it with many other things, with success, with knowledge, with position or power, but none of those things satisfy. Only a living relationship with God through Jesus Christ can quench that spiritual thirst. Jesus himself invited, if anyone thirsts let him come to me and drink. When that thirst is awakened, and a person comes to Christ, the Spirit bears witness within that this is true.
It is also wise that you noted education alone does not make a person righteous. The Bible speaks of those who have a zeal for God but not according to knowledge, who are ignorant of the righteousness God provides and try to establish their own righteousness by their works or by keeping the law. No one can be good enough for God on his own. The righteousness that God accepts is not earned by learning or by good deeds, it is imputed through faith in Jesus Christ. His righteousness is given to us when we believe in our heart that God raised Jesus from the dead and confess him as Lord. That is the only righteousness that will stand.
At the same time, Scripture warns us to guard our own hearts and to leave judgment to God. God looks on the heart while we only see the outward appearance. We are quick to judge others, but God has reserved judgment to himself and he will judge according to truth, because he alone knows what is in the heart. Knowing the truth brings responsibility to obey it, and we should examine our own motivations, keeping our hearts with diligence, for out of the heart flow the issues of life. Your humility in saying you do not wish to boast or to look down on others is important to keep, recognizing that all have sinned and fall short of the glory of God.
Do not blame God for the evil and brokenness you see. Death, injustice, and the disregard for human life and honest communication are the result of sin in this fallen world, not the fault of God. Our hope is in redemption. Just as the law provided for a kinsman to redeem, God has provided a Redeemer in Christ who shed his blood for our redemption. We groan and long for that full redemption, and we pray and work toward that day while trusting his lovingkindness and truth to preserve us.
Continue to pray as you are praying, with compassion and without self righteousness. Pray that God would cover those you mentioned with mercy, that he would grant them repentance, that they would see their need for the Savior, that they would hunger and thirst for his righteousness and be filled, and that they would worship him in spirit and in truth. Pray also that your own life would be like light, creating in others a thirst for Christ rather than driving them away.
May the Lord give you peace as you entrust these people to him, and may he answer your prayer by drawing them to himself, forgiving their sins through the blood of Jesus, and teaching them to walk in righteousness, mercy and truth.