Now assume I end up having leaving the country: do I have to pay taxes over my earnings back in Japan?Regardless of whether you leave the country or stay there, you will have to pay taxes on income in Japan. If you leave during the tax year, you will have to inform the tax office and pay outstanding taxes, I assume.
Most EU countries should have tax agreements with Japan, which assure that you don't get double-taxed.
Basics about taxes in Japan:
http://www.japan-guide.com/e/e2206.html
Maybe one is required to pay taxes when it comes to large amounts of money?
No, you have to pay taxes on any amount of income! Only if the amount is really small, you might not have to pay anything.