Question: Why did the tech company that manufactured David stay based in Manhattan? Considering that it's flooded. Seems a little impractical.
Question: They say David's mom is dead because 2000 years have passed. Does David not understand that humans can't live that long?
Answer: Yes, he knew humans die. He asked mom if she would die, she said yes, but not for a long time...50 years. David asks Teddy "is 50 years a long time?" and Teddy says "I don't think so." He denies she is dead/can't be brought back for more than a day b/c that is not the answer he wanted.
Answer: Being robotic in the first place and ending up at the exhibition where old robots are destroyed probably told David that things die, through the actions of others. It's plausible he may not know any different, still functioning 2000 years later when found under water with his bear. It does come as a shock to him to learn everybody he knew has gone, so I'd say no, he didn't know humans (and his mum) will die. It's shown David can learn and retain information, and to be honest it's not really the sort of conversation you have with a child until it's strictly necessary anyway.
Question: So, what happens to David and Teddy after the movie is over? Wouldn't they be alone on Earth after David's mother dies again?
Answer: It is implied that David dies after spending the day with Monica. The narrator says that he falls asleep and goes to "that place where dreams are born" which could be interpreted to mean the afterlife. Teddy's fate is never mentioned. However, the words of the narrator could also be interpreted literally, and David simply falls asleep and has a dream. It's up to the viewer to decide how they view the ending.
Question: Why did Professor Hobby, at the beginning of the movie, tell the Mecha to undress?
Answer: The Mecha was in a room full of strangers, and yet, because it had no feelings of shame (no feelings at all was the point), it undressed without any concern of onlookers.
Chosen answer: To show how completely obedient the mecha are and that there is nothing to be afraid of when it comes to them.
Answer: The owner/inventor of the company may have kept the doors open in Manhattan to see if any of his products would return 'home'. He seemed to be very pleased that David had returned and was interested in finding out why. I got the feeling the AI's creator was hoping for a sign that the instinct to return was something novel and not just a predictable result of their original programming.