My name is Natasha Romanoff. I'm look to be in my mid-twenties, but I was actually born circa 1928. I am know as the "Black Widow" in the Avengers. I'm a kickass fighter, who excels in really any type of combat.
She does know from experience. He trained her in the Red Room. He doesn't remember her, and we've seen no evidence in the MCU that she remembers him from the Red Room, but these two DO know each other.