1) My best friend lives next door to me, and we go to school together.(правильно, если не считать запятой)
2) Excuse me, where is the next bus stop? (правильно)
3) The cinema is a bit farther (on- лишнее) along this road, next to the bank.
4) The nearest train to Saint Petersburg leaves at 6:30.
5) Further education is the education you get after leaving school.
6) They think the Sun goes around the Earth. What is next?
7) If you travel farther north, you will be able to see some very beautiful places of wild nature.
8) What are they going to do in the nearest future? (правильно)