Shana Tova means, literally, A Good Year.
Many Jewish festivals are celebrated over two days because, originally, before the days when the calendar was fixed and everyone had access to a calendar, the priests in Jerusalem would light a beacon to indicate the begining of the festival, and watchers on hills around would see the beacon and light their beacon and so on. So the message would be transmitted that the festival had begun. But once Jews began living outside Israel there was concern that the might get the message too late, so many of the holy days were celebrated over two days instead of one, just to be certain. Nowadays a lot of festivals which are two days long outside Israel are only celebrated on one day in Israel.
Sssandy, after Rosh Hashannah come ten days of repentance and prayer (called, in English, the Days of Awe), followed by Yom Kippur, whcih is our Day of Atonement. After that the joy and celebration begin, and Succot is indeed joyful festival.
Wintersun, when should we wish Eid Mubarak, and what does it mean?
I love all these differences between us, and wish that more parents would come to the schools to tell the children about the different ways of life, and to let the children taste (literally!) the variety. I'm sure that if other religions and ways of life were more familiar to us, there would be less hostility.