It is entirely possible that all of the answers I am about to type out will be obsolete by the time you read this, because of something else you have read that has helped to shape your beliefs or some other reason but I think I can help you grasp and define these things a bit more concretely. I’ll try to number my paragraphs to directly respond to each of the 7 primary paragraphs you’ve presented so you can easily see the context of what I am saying.
[1] To have faith is to believe and (metaphorically) be grounded like a tree or sign - when the wind blows it may bend a little, but it does not move much and almost always returns to its original position. Look at what the Lord tells the father of a child who has a spirit: "Jesus said to him, “If you can believe, all things are possible to him who believes.”
Immediately the father of the child cried out and said with tears, “Lord, I believe; help my unbelief!” When Jesus saw that the people came running together, He rebuked the unclean spirit, saying to it, “Deaf and dumb spirit, I command you, come out of him and enter him no more!” (Mark 9:23-25 NKJV) Don’t let this “I believe; help my unbelief!” deter you or confuse you, this is a man who came to Jesus hearing that he performed miracles and had hope that Jesus would help his son, this man had enough faith to bring his son to Jesus for even the possibility of being healed (as we all bring ourselves to Jesus hoping that he will heal us), and then Jesus very frankly tells him to believe more, because there is doubt in his heart. So what does the man mean by the “help my unbelief”? He is admitting he is weak, he is admitting there is doubt that troubles him but he has also showing that he believes in the help Jesus offers and so in one act cries out “I believe; help my unbelief” - and from that is the basis by which Jesus heals his son and from the healing of his son, the father leaves with his son having a much more grounded and deep belief, therefore a deeper faith.
[still 1] This leads up to your question about asking without wavering. The simple answer is “if you ask then you have not wavered” because your faith carried you to ask. You may have some doubt but the essential aspect of the issue is that you asked even though you had doubt (which means that the doubt wasn’t enough to stop you). Once again, look at the verse I quoted above, where the man says “I believe; help my unbelief” - he has doubt but that doesn’t stop him from asking. Eventually, you will be able to put your doubts to rest as you gain knowledge so do not stop seeking.