Pay attention to the sign of the Lost and Found office that Paddington is sitting in front of at the train station. The "found" part of the sign has gone out... until Mrs. Brown walks up to him and says hello. Then, it flickers and blinks on brightly. Paddington was lost, but now he's been found, even if no one involved quite realises it yet.
Mr. Gruber's story does not sound like he was sent away during the Bombing of London. It sounds more like he was sent away from home via Kindertransport (a system that took Jewish children out of dangerous countries such as Germany, Austria, Poland, and Czechoslovakia and resettle then in England). It's highly likely that he lost his parents due to the Holocaust.
If bears are sapient, who knows what other animals also are... it is entirely possible that the Natural History Museum is full of stuffed specimens of sapient beings.
