AWe have no way of knowing, as he never asked the question. As stated in the above question; It's entirely possible he was suspicious and simply toying with her. It's also possible he was considering confronting her about his suspicions but at the last moment decided not to act on them.
AThe following people are involved in the shoot out: Bridget Von Hammersmark, Hugo Stiglitz, Wilhelm Wicki, Archie Hicox, Major Hellstrom, Wilhelm, the German soldiers identified by their game cards on their foreheads; Winnetou, Mata Hari, Edgar Wallace, Beethoven (Female Soldier), Eric the Bartender, and Eric's daughter Mathilda the waitress. Things are very confusing given that the events of the main shootout all happen in under 35 seconds:1. Stiglitz starts things off by telling Hellstrom to say "auf Wiedersehen" to his Nazi balls, then shoots him in his groin.2. Hellstrom then shoots Hicox in turn and hits Bridget in the leg, who falls backward in her chair, while Hicox falls backward and returns fire at Hellstrom.3. Stiglitz then stands up and repeatedly stabs Hellstrom in the back of the head, pinning his head to the table.4. Wicki stands up and shoots Winnetou in the back at least twice.5. Beethoven shoots Stiglitz in the back.6. Mata Hari shoots Wicki in the stomach.7. Stiglitz turns and shoots Beethoven four times in the torso and then also shoots Edgar Wallace in the heart, killing them both.8. Wicki shoots Mata Hari in the heart.9. Eric shoots Stiglitz with a double-barreled shotgun, killing him. [Note: this is the only shot that isn't definitive as there is an extreme close-up of Eric while he takes aim, but when there is a wide shot of him, he appears to be aiming in Stiglitz' direction. It was theorized he was shooting at the Germans, but Wicki wouldn't have shot him if that was so].10. Wicki shoots Eric in the head.11. Wilhelm blindly guns down Wicki and Mathilda with his MP40 submachine gun. [The way the final shot is filmed, it's possible Wilhelm also shot Mata Hari in the back, or it could have just been editing of Wicki finishing him off.]12. After Wilhelm agrees to surrender to the Basterds, Bridget retrieves Hicox's pistol and fires four shots at Wilhelm, hitting him at least twice in the chest, killing him.
AViewers have suggested that (1) Landa (Christoph Waltz) admired Shosanna's will for survival, (2) the distance between them was too great for an accurate shot, (3) Landa wanted her to spread the rumors of him being "The Jew Hunter", (4) he had no doubt that he could track her down at a later time, and (5) he didn't want to shoot her in the back (mentioned in the script, but left out of the movie). In the 'Cannes Cut', he informs his soldiers that she will freeze to death anyway in the coming winter.