Does country of author influence the rejection of research paper
I am not sure that I ever seen any substantiation statistical research on it, but it is definitely believed that researchers from some countries  are under pressure to generate large quantities of research papers, but not necessarily under the same pressure regarding the quality of their research. The lists are subjective and vary from one researcher to another, but often include China, India, Russia and post-Soviet countries, etc.  So, yes, peer-reviewers may have a subconscious bias against research papers from these countries. This bias may be further amplified by the language barrier &mdash; if the paper is written in sub-par English, it may reflect on the perception of research explained in the paper.

However, reviewers should not allow their bias to affect their decision and there are systems in place to ensure they don't. Good journals have good policies which encourage reviewers to work with their bias and also involve a diverse panel of reviewers to consider the merits of the paper more objectively.

Regarding your last statement, yes, it is always good to carefully check your paper before submission and stress the novelty and usefulness of the proposed research idea.