Well, obviously you don't define faith the same way I do.
In a religious context faith means believing without evidence. Not talking about proof beyond doubt, just any evidence. There is none, so there is no reason for me to believe any of it. And extraordinary claims require a Bit more evidence than "an ancient book, written by people who hardly knew anything about how the natural world works, says so.
You didn't go to this surgeon on faith. You had evidence that he was a competent doctor since your relatives had good experiences with him.
If you had went to him, trusting he could operate on you well enough, without ever knowing if he really is a medical doctor after screwing up the rest of your family already, then I would call that faith.
The way it went, you trusted him on good measurable evidence. You can Call it faith if course, but it is not what an atheist means when talkibg abour faith in god and I doubt you believe it the same thing.
Your unique flower is different than god, too. I know flowers exist, what general properties they usually have and that there are probably many flower species that I have never Seen before since new ones get discovered all the time.
So in this case I have reason to tentatively take your Word for it.
Though I might ask you for a picture you might have taken or the location if I want to experience it myself.
If you can't provide any, I will still accept as a likely true anecdote but can otherwise remain happily ignorant about the flower.
Faith in a spouse has nothing to do with his/hers existance, but whether or not him/her cheating on their partner.
Trust in friends is a property of friendship, otherwise they wouldn't be y friends. Again, has nothing to do with their existance.