How does a person become 'a child of God'?
The way to believe in God is by directing our lives at being in His likeness by being a doer of His character traits in obedience to His law, and it is by this faith that we become a child of God. For example, by being a doing of good works in obedience to God's law we are testifying about His goodness, which is why our good works bring glory to Him (Matthew 5:16), and by testifying about God's goodness we are expressing the belief that God is good, or in other words we are believing in Him, and the same is true for God's other character traits. The way to believe that God is just is by being in His likeness through being a doer of justice, the way to believe that God is holy is by being a doer of His instructions for how to be holy as He is holy, and so forth. This is also why there are many verses that connect our belief in God with our obedience to Him, such as in Revelation 14:12, those who kept faith in Jesus are the same as those who kept God's commandments.
Your delineation for observance or non-observance of laws specific to matters of gender do not reflect the rudimentary understanding of anyone capable of comprehending the male/female physicalities and I am certain the Israelites did not exhibit confusion concerning their laws either.
It was just an example to illustrate the point that there are legitimate reasons for not following certain laws, which is not what James 2:10 is referring to.
Your personal mashup of grace and law is not biblical.
Grace is a gift and gifts can't be earned, so grace is incompatible with works insofar as they are done to earn a wage (Romans 11:6), however, works can be done for reasons that are compatible with grace. For example, a gift can be the experience of doing something, such as giving someone the opportunity to experience driving a Ferrari for an hour, where the gift intrinsically requires them to do the work of driving it in order to have that experience, but where doing that work contributes nothing towards earning the opportunity to drive it.
In Psalms 119:29-30, he wanted to put false ways far from him, for God to be gracious to him by teaching him to obey His law, and he chose the way of faith by setting it before him, so this has always been the one and only way of salvation by grace through faith alone.
In Exodus 33:13, Moses wanted God to be gracious to him by teaching him to walk in His way that he and Israel might know Him, and in Matthew 7:23, Jesus said that he would tell those who are workers of lawlessness to depart from him because he never knew them, so the goal of the law is to teach us how to know God and Jesus, which is His gift of eternal life (John 17:3), and which again is the gift of salvation by grace through faith.
In Genesis 6:8-9, Noah found grace in the eyes of God, he was a righteous man, and he walked with God, so God was gracious to him by teaching him to walk in His way and he was righteous because he obeyed through faith. In Romans 1:5, we have received grace in order to bring about the obedience of faith.
In Ephesians 2:8-10, we are new creations in Christ to do good works, so while Paul denied that we can earn our salvation as the result of our works lest anyone should boast, being made to be a doer of good works in obedience to God's law is nevertheless a central part of God's gift of salvation.
In Titus 2:11-13, our salvation is described as being trained by grace to do what is godly, righteous, and good, and to renounce doing what is ungodly, so doing those works has absolutely nothing to do with trying to contribute anything towards earning our salvation, but rather God graciously teaching us to be a doer of those works is part of His gift of salvation. In Titus 2:14, Jesus gave himself to redeem us from all lawlessness and to purify for himself a people of his own possession who are zealous for doing good works, so the way to believe in what Jesus spent his ministry teaching by word and by example and in what he accomplished through the cross is by repenting and becoming zealous for being a doer of good works in obedience to God's law (Acts 21:20).
God desires us to be conformed to the image of His Son and that is a process. Salvation happens in the moment; sanctification is our walk with Christ in the power of the Holy Spirit as scripture reveals. You do not state when you accepted Christ.
Sadly, your confusion with the law being a part of salvation negates the very purpose of Christ's sacrifice on our behalf. The only way you could possibly arrive at your personal beliefs, which you reference throughout your post(s), is by ignoring a good many passages of scripture that detail why the law has not saved and will never save anyone, no exception.
The Son is the radiance of God's glory and the exact image of God's likeness (Hebrews 1:3), which he expressed through his works by setting a sinless example for us to follow of how to walk in obedience to God's law, so the way to believe in, accept, and be conformed to the likeness of the Son is exactly the same as the Father, namely by being a follower of his example. Aspects of God's character are the fruits of the Spirit. Jesus saves us from our sin (Matthew 1:21) and sin is the transgression of God's law (1 John 3:4), so while I completely agree that we can't earn our salvation as the result of our obedience to it, Jesus graciously teaching us to bear the fruits of the Spirit by being a doer of God's law is intrinsically the way that he is giving us his gift of saving us from not being a doer of it.
According to Titus 2:14, becoming zealous for doing good works in obedience to God's law does not negate what Jesus accomplished through the cross, but rather it is in in accordance with it, while the way to negate what he accomplished would be to return to the lawlessness that he gave himself to redeem us from.