Okay, this is kind of a trap, but only to show what faith is, and to explain again, how it works through your examples.
I sought God long and hard on this, while search the scriptures, as I was led.
When someone tells you something about yourself, such as a prophet prophesying over you, they receive knowings in their spirit man, as well as visions, from another source, like some of you have witnessed. And like many of you can attest to, you can or are able to put what you know into words, just like the prophets do.
It is the same process as that of a prophets. You have a knowing and you simply say it like you received it.
This information/knowing is put or told to your spirit man from another spirit, such as the Holy Ghost, which is in your heart.
When you know something, it causes you to believe with all your heart, and prevents you from being able to doubt, which is the perfect ingredient for real faith or for the law of faith to take effect or manifest in the natural, even as it is written.
If any man lack faith, let him ask of God who giveth to all men liberally, and upbraideth not, but let him ask in faith NOTHING WAVERING. And goes on to say of those who waver, "but let not that man think that he should receive anything of the lord."
When you act on what you know, before you see any outward signs, whether it be through speaking or acting on said knowings, that which you know will absolutely come to pass, EVERY TIME.
That is one aspect of faith and how it works.
Obviously, many of the knowings don't have to be acted on for them to come to pass, but there are those which do require action on you part. But the point I wanted to get across is that it causes real faith in the heart of the one who knows. It eliminates hopeful or wishful thinking, which causes it to manifest. It is the law of faith and it works every time.