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?
Japanese people
Language.
The Japanese language is a Japonic language that is related to the Ryukyuan languages and was treated as a language isolate in the past. The earliest attested form of the language, Old Japanese, dates to the 8th century. Japanese phonology is characterized by a relatively small number of vowel phonemes, frequent gemination, and a distinctive pitch accent system. The modern Japanese language has a tripartite writing system using hiragana, katakana, and kanji. The language includes native Japanese words and a large number of words
History of Japan
The history of Japan covers Japan and its relation to the world. It is characterized by isolationist, semi-open and expansionist periods.
Please see the era classifications for details of each era.
The very first human habitation in the Japanese archipelago has been traced to prehistoric times around 30,000 BCE. The Jōmon period, named after its "cord-marked" pottery, was followed by the Yayoi in the first millennium BC when new technologies were introduced from continental Asia. During this period, the