对联is an art of Chinese language and somehow wonderful but difficult to be translated into other languages. Here I try to traslate the sentences above in the free way.
1、一元复始,万象更新。
A new year begins and everything becomes vigorous.
2、书山有路勤为径,学海无涯苦作舟。
Diligence is the path to the mountain of knowledge, hard work is the boat to the endless sea of learning.
3、松竹梅岁寒三友,桃李杏春风一家。
Pines, bamboos and plum flowers(梅花?) are three friends who withstand the cold in winter. Peach flowers, plum flowers(李花?), prunus flowers are family that enjoy the breeze in spring.
4、八百里湖山,知是何年(not 人)图画?
十万家灯火, 尽归此处楼(not 亭)台。
(seeing from the top of the mountain)
Lakes and mountains lying abreast for 8 hundred miles, do you know when this picture was drawn?
Lights twinkling in hundred thousand families simultaneously, all of them were seen at the tower I'm inside.