I am in the process of writing a research paper in Computer Science. Are there any free tools/browser plugins/web sites/latex plugins that would help me improve my English? I am looking for some nice applications that give examples of correct English usage.
There are no computer programs that are going to make you a magnificent writer. The only way you can learn to write is through lots and lots of practice.
The first thing you're going to want to do is read and read a lot. Read fiction, read non-fiction, read writing textbooks. Visit your local library and read all different sorts of books to get a good grasp on the English language.
Then you're going to want to write, rewrite, and write some more. It helps if you work with someone with experience in the writing/editing field. They'll be able to point out any mistakes you make, help you understand those mistakes, and make sure you don't make those mistakes again.
Writing is a slow and painful process. There are no shortcuts and even in the technology age, a computer still cannot teach you how to write well.
Public library is the cheapest source. In other words: read, read and again - read. Reading books, newspapers and magazines is the best way to improve someone's language usage. Any language.
Try to avoid web resources, particulary twitters, facebooks and other shout-and-bark sites. Even most of weblogs are utilising some bastardised mutation of language, so I cannot recommend them as correct sources.