Finnish is not related to Japanese, though there are so many similar-sounding words that it is a source of humor in Finland and to a lesser extent in Japan. These similarities are coincidental and the similar words mean completely different things. I know only one word that looks similar and means the same thing: matto, a mat. Of course my knowledge is limited and there may be other words that look similar and mean the same -- usually loanwords.
The most fascinating in my mind is the Japanese expression "unten suru"; in Japan it means something as prosaic as "to drive, operate", but in Finland it means "the sorrow of the dreams" (unten suru or unien suru).
Yes, the Estonians, Finns and Hungarians came from Siberia -- thousands of years ago.
Why are so many people in the North blond? "Naturally-occurring blond hair is primarily found in people living in or descended from people who lived in the northern half of Europe, and may have evolved alongside the development of light skin that enables more efficient synthesis of vitamin D, due to northern Europe's lower levels of sunlight."