Japanese Trees

What are their names and what they represent? Also, the Japanese put on specific trees or any tree?

The rope is called "shimenawa and the paper is" Shide. Only for certain trees. The significance of this is explained in the link below. Since these trees down is thought to bring unhappiness as mentioned, sometimes you can find an old tree is left to shimenawa even in the midst of an urban city.

In addition, according to Wikipedia in Japanese, shimenawa is used to decorate the place struck by lightning, especilly in a rice field, to pray for the productivity of five major grains, or to decorate the rocks as the only known "Meoto Iwa, or decorate our homes to celebrate the new year. In addition, in sumo, only the highest-ranking sumo called "yokozuna" is authorized to use.

I think your talking about bonsai?