Let us bring your requests before the Lord, seeking His will and guidance in all things. Firstly, we are reminded of the words of Jesus in Matthew 7:7-8 WEB, "Ask, and it will be given you. Seek, and you will find. Knock, and it will be opened for you. For everyone who asks receives. He who seeks finds. To him who knocks it will be opened." It is wonderful that you are coming to God with your petitions, but let us also remember to trust in His timing and plan.
Concerning your need for a vehicle, we pray that God's provision and timing would be evident in your life. Remember that God knows your needs and cares for you, as seen in Matthew 6:31-33 WEB, "Therefore don't be anxious, saying, 'What will we eat?', 'What will we drink?' or, 'With what will we be clothed?' For the Gentiles seek after all these things, for your heavenly Father knows that you need all these things. But seek first God's Kingdom, and his righteousness; and all these things will be given to you as well."
Regarding your court case and custody battle, we pray for justice and wisdom to prevail. We ask God to grant you favor in the court's eyes as well as given to King Solomon in 1 Kings 3:28 WEB, "All Israel heard of the judgment which the king had judged; and they feared the king: for they saw that the wisdom of God was in him, to do justice." Yet, we must also consider the children's best interests and pray for their well-being above all. We are called to act in love towards them and ensure that we are living in a way that honors God.
As for your applications, we pray for open doors and smooth processes if they align with God's will for you. Trust in the Lord and lean not on your own understanding as mentioned in Proverbs 3:5-6 WEB, "Trust in Yahweh with all your heart, And don't lean on your own understanding. In all your ways acknowledge him, And he will make your paths straight."
However, we notice that your prayer does not mention the name of Jesus Christ. It is only through His name that we have access to God, and there is no other name by which we can be saved. As it is written in Acts 4:12 WEB, "There is salvation in no one else, for there is no other name under heaven that is given among men, by which we must be saved!" Let us keep this in mind as we pray together.
Finally, let us pray together:
Heavenly Father, we come before You in the name of Jesus Christ, lifting up this person and their requests. Lord, provide for their needs according to Your will and timing. Grant them favor in the court's eyes and wisdom for all involved in the custody battle. Be with their children, and let Your love and protection be evident in their lives. Guide the outcome of the applications, and let Your will be done. Help us all to trust in You and seek Your face in all we do. In Jesus' name, we pray. Amen.
Prayer Focus: God, Thank You. Thank You for loving me. God, I ask You in Jesus’ name bless me with everything that I stand in need of and everything You want me to have. Bless me to know You in truth, fall in love with You with all my heart, mind, soul, body, and strength and never fall out of love with You. Bless me to have an ever growing closer stronger, more intimate relationship with You. Bless me with the love, desire, strength, and the spirit of obedience to always delight myself in You, seek first Your kingdom, and Your righteousness. Help and strengthen me God to always respect and obey You. Bless me to trust You with all my heart, acknowledge You in all my ways, and lean not to my own understanding. 
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