I am trying to create a page dynamically i.e on creating a page at a path, a copy of the same page should get created in the given path. The pages should also be dynamically linked to each other i.e a change in one should get reflected in another and vise versa.
Of course this is possible. You can create pages via the PageManager API, but from then on you are on your own. You need to create the resources for the individual components on your own, also providing the correct content into the right properties etc. To make this work well you need to understand how your pages are structured and know your components.
Well, there are ways to do that, but let me first ask the question why you want to do that. Having the same page available at multiple locations rarely makes sense per se, so there must be a business reason which I would like to understand first to give you a good recommendation.
I am trying to understand your requirement here little more clearly. " i.e on creating a page at a path, a copy of the same page should get created in the given path" By this do you mean that when the author creates a page manually via siteadmin ; you want to create a copy of the same page via code ?
What is the issue you are trying to address here ? I don't think keeping a copy of the same page under the same path is right way to do it ? There should be a better way to do . If you can share the problem you are trying to solve ?