The history of Japan is fascinating. There is evidence of the first habitation in Japanese archipelago in prehistoric times.
How interesting.  How long has Japan been around with the same native people?
I'm not sure but during the 4th century and the ninth century, a centralized government was created.
That is awesome.  Can a lot of Japanese people trace their ancestry that far back?
They probably can. Around 129 million people are of Japanese descent and about 125 million of them live in Japan.
How do they display their culture whether it be in their homes or public spaces?
I'm too familiar with that but I do know the japanese language is related to the ryukyuan languages.