Does the rise and fall of one country effect other countries around the world?

Yes. Countries are interdependent on one another and lots of things happening in one country affects many other countries. So when a country rises or falls, it will affect other countries. A country may be overtaken by a rising country or may get free of a falling country. Trade may grow with a rising country, but fall with a falling country, and so affect the economy of many countries. The culture of strong countries can spread into other countries as it becomes stronger. A rising country may gain more influence and help some countries. If a powerful country falls, its friends lose some of their influence and support. So, yes the rise and fall of countries do affect other countries for many reasons and in many ways.