I agree that all three are grammatical, however the first is generally phrased as “Did you know the lady is in the car?” and it would only work if there was a specific lady to be spoken about in the current context. What is the difference between “Do you know…” and “Did you know…”? Is it hard for one to come up with a clear concept. I think I’d tend to use the first one if I really didn’t expect the person I’m talking to know that and I’m trying to impart the information to them. On second question, I’d more likely use if I’m just inquiring about their understanding and so I’m trying to get information from them on their state of knowledge, rather than trying to give information to them about “the lady” in the

car.