Peer review process in a math journal
My pet peeve as a reviewer is authors that ignore reviewer comments. If you were asked to revise the paper and did not listen, that's a desk-reject in my book. Part of the scientific method is the ability to improve one's work based on peer review. If you cannot do it for whatever reason, then expect a series of rejection.

Is it possible that my paper is considered as a crackpot ? I know that my writing is not up-to the professional level.

Yes, it's possible. Nowadays, proper academic English is the medium of communication in most academic papers (if you had lived 500-600 years ago you'd have needed to write in Latin); you need to conform to this standard before your paper has any chance of being published in a respectable venue.

I am not belonging from a well known place and I am also unknown in research. Does this create any negative impression?

I would like to tell you that only the content of your writing matters, and not your institution/rank etc., but that's unfortunately not true. While this varies between reviewers, I do believe that papers originating from well-known academic institutions are held in better regard. Of course, if you submit your paper to a respectable venue then it would be judged primarily based on its contents. However, the combination of improper English and unknown institution does not help.

I am expecting to apply in graduate math program. Will the admission committee take my paper seriously if I cannot publish it by that time?

That depends. There are plenty of places where you can upload a copy of your work for the public to see (ArXiv is one notable example). You can also try and publish it in a workshop on combinatorial game theory, so that you get a chance to solicit feedback and present your work. This will help get some visibility for your work, and perhaps signal to potential advisors that you are serious. If you send your manuscript to specific advisors you'd like to work with, and are in a position to judge the content of your work, they may look past the stylistic issues and see whether there's any potential to your work.