How does already having an academic scholarship affect graduate school admissions? I'm currently applying to Grad school- mechanical engineering-and have a full academic scholarship to continue my education from the government. 

Does this make it easier for me to gain acceptance to top schools like Stanford and Carnegie for masters? I'm doing the GRE in 3 weeks, but will I still need a 165+ in the math section to be admitted just like everyone else? 
My GPA isn't stellar either. I guess the only stellar thing about my application is that I already secured funding.
Having your own funding may help, e.g. if you are a good match for a faculty member who has an interest in supervising a PhD student, but does not have enough funding to support one at the moment. But no department wants to waste time and resources (e.g. supervision resources, for example) on a student that is not capable of meeting standards in the department. And given that a department's PhD students represent its "brand," no department wants to admit a student whose work will reflect negatively on the department.

So yes, even if you have your own funding, you still need to show the department you're applying to that you're capable of meeting their standards.