Freelance writing is a difficult field to break into. It doesn't matter how good you are, you must first be recognised by editors and publishers and I should think that will take much more than six months.
As a non-native speaker, would I be able to be a professional freelance English writer within 5-6 months while greatly improving my English writing skills?
I don't see why not. Depending on the subject matter it can be easy to difficult to format and use the appropriate "words" .