The brief response is yes, God does hear every thought, idea, prayer, motivation, secret desire, urge and true feelings we ever experience. But then again, God is God, we are not. In His divine and Holy wisdom He knows the true intent and true reasons why we say and do the things we do. And in His wisdom He provides us the grace and power to meet whatever issue or need we have.
As the author of all creation, He made us, you and me. And knows full well that at times we can be vain, arrogant, short tempered, and judgmental. And the good Lord also knows how to deal with our pains, emotions, hurts and feelings. It is not that we pray to God “dear God, please have old so and so have a flat tire”, but at times we hold grudges, bad feelings and not wish certain people the best. That’s human nature, we are people of the flesh far more than we are saints or pillars of the community. But God in his mercy and grace understands us and will love us, even when we are less than lovable.
The response of the Christian in the face of evil or bad people has not changed. We are to pray for those who seek to do harm and place ultimate justice issues in the hands of the Lord for final adjudication. We may at times in our hearts wish bad things to happen to bad or evil people, but at the end of the day God will have the final word on that matter, not us. And God’s will and justice is both right and sovereign. Human justice, human desires and that of the Lord are always two different things. Thank the Lord for that.
So yes, God does hear all our prayers, the well formed ones and at times the incoherent and confused. By his grace and mercy his love and mercy is poured out on his covenant people and his church. Christians are not perfect, never have been, we have only been forgiven. Praise God for His mercy and grace.