Short answers, pulled from the story.
The Roman Republic settled on January 1 as the start of the year in 153 BC. This date was chosen because it marked the traditional annual convening of the Roman Senate and the assumption of civil office. The Julian calendar introduced by Julius Caesar in 45 BC solidified this date as the standard.
Great Britain recorded the year 1706 in England while Scotland recorded 1707 because Scotland adopted the Modern Style of January 1 in 1600. England continued to use Annunciation Style on March 25 until the Calendar Act of 1750 unified the British Empire under the Gregorian system. This created a decade-long discrepancy that confused historians and genealogists alike.
The Chinese New Year falls anywhere between January 21 and February 21 of the Gregorian calendar. It occurs every year on the new moon of the first lunar month. This lunisolar calendar must be restarted annually on the first, second, or even third new moon after the winter solstice to stay aligned with the solar year.
The Iranian New Year Nowruz occurs on the day containing the exact moment of the Northward equinox, which usually falls on March 20 or 21. This event marks the start of the spring season and is passed on to Central Asian countries where it is known as Nauryz. The celebration is usually held on March 22 in those regions.
The Islamic New Year occurs on Muharram and moves through the Gregorian calendar by about eleven days earlier each year. This shift happens because the Islamic calendar is based on 12 lunar months amounting to about 354 days. Two Islamic New Years can fall within a single Gregorian year, such as in 2008.
The Calendar New Style Act 1750 went into effect on the 3rd of September Old Style or the 14th of September New Style 1752. This act converted all parts of the British Empire to use of the Gregorian calendar and declared the civil new year to be January 1. It marked the end of a long period of calendar confusion and the beginning of a unified timekeeping system across the British Empire.