Are you then saying that the centurian and the gentile woman were people properly trained in theology and after much study of the scriptures concerning the nature of God and salvation they then placed faith in Christ???? Or was their faith a leap in the dark?????
I highly doubt either were trained in theology. Some of your greatest skeptics are highly educated people, while great faith usually belongs to "simple folk".
It is certain both the Gentile woman and centurion had heard of the fame of Jesus, perhaps they had seen the great crowds that followed him, perhaps they had even witnessed miracles he had performed. Obviously they had some knowledge of the Jewish religion and at least knew of the promised Christ.
Faith in Jesus was that he was loving and merciful and would help them if they applied to him. Both the Gentile woman and centurion seemed to know that Jesus came to the lost sheep of Israel only, but both believed he would also show mercy to Gentiles. This is faith.
According to your definition of faith there can be NO CERTAINTY of salvation in this life. No Christians can absolutely say "I KNOW whom I have believed and am PERSUADED..." or "I write these things unto you that beleive.....that ye might KNOW" or "I KNOW my redeemer...."
The kind of faith you have described and defined is UNBIBLICAL and saves N
NE because it has absolutely no relationship to saving faith in Scripture. Saving faith in scripture is a direct result of IMMEDIATE and DIVINE revelation IN THE HEART of true believers so that there is no doubts whatsoever, so a true believer can say 'I KNOW" Jesus Christ as "THIS IS ETERNAL LIFE that they might KNOW thee..." Your kind of faith provides no such certainty.
I am not saying that we cannot have assurance, we certainly can and should have assurance. Yet, no man will know for an absolute "certainty" until he is standing in heaven.
Faith is the evidence of "things not seen". You cannot have absolute certainty of something not seen.
Rom 8:24 For we are saved by hope: but hope that is seen is not hope:
for what a man seeth, why doth he yet hope for?
You don't hope or have faith for things you can hold in your hand and see, things you can hold and see you have certainty of. Faith is waiting and believing what you cannot see.