I'm almost positive he knows it's her.
Those little things he says are just like his personality to poke at her. Inquiring deeper than most people about her aunt and uncle and how they died. Ordering milk for her knowing she had been taken in and saw her family murdered at a dairy farm, watching her as he said it.
Jews in hiding weren't hiding because no one would notice them, they probably made the mistake of leaving behind pictures, Thethe state probably had photo ideas. And Landa doesn't seem like the type to forget a face.
And that last thing he couldn't remember that must have just not been important. He ended the movie betraying Hitler. That's not a split second-second decision. He had probably known at that time the state of things in the war and was planning his betrayal at that time.
Why exert himself more than needed?