Hi Alexandra,
The Church New Year still begins on 1 September, that hasn't changed. In some ways it is nice, to be able to observe a new year quietly and peacefully, seperate from the hustle and bustle of the worldly new year celebrations. But (at our Church) we also observe the January 1 New Year too - but it is quite funny - first we have (Gregorian) New Year (though not at Church) which I jokingly call 'New' New Year, then on the 14th the Church has New Year (which I call 'Old' New Year), then on 14 September is the Church New Year.
The reason why Russia didn't change until 1918, was that until the Bolshevik takeover, Russia was an Orthodox country. The Gregorian calendar might be astronomically wonderful, but it absolutely and utterly mucks up the observance of Feasts in the Church, in particular Easter, which according to Church canons, both Catholic and Orthodox, must not occur before the Jewish Passover. However with the Gregorian calendar, Easter is occurring more and more often before Passover, and this trend was noted with some degree of alarm in a (western) book from the 19th Century I read some time ago. (I can't remember the details of the book though). With the Julian Calendar, Easter never occurs before Passover. Some of the Orthodox countries changed to a varient of the Gregorian in the 1920s (eg Greece), but this caused huge controversy and division - and in Greece this is still the case, there are Old Calendar Jurisdictions and new calendar ones - I understand they tried to make Old Calendar ones illegal. However, even Churches on the 'New' calendar use the old calendar for Easter and its associated feasts and fasts. (This creates another problem though in that sometimes the Apostles Fast which starts a week after Pentecost) ends up becoming a 'negative' fast of minus two weeks or something, as the fast starts on the old calendar but finishes on the new, and the Day of SS Peter and Paul can fall on the new calendar before the fast is due to start on the old.
There are many other problems involved with using the new calendar as well, but it is not my place to pass judgment on its merits or defects.
The Russian Church, Serbian Churhc, Japanese Church etc all still use the old Calendar. I think the majority of Orthodox believers are on the Old Calendar, though the majority of Orthodox countries are on the new, but i am not sure of my statistics here.