Coming from a "No Name" University outside the US, what are my chances for admission Background Information
           I would soon be graduating with an engineering degree from a "no name" university somewhere in Nigeria. My performance during my degree was above average. I am hoping to apply for a PhD program in US.
The professors with whom I interact with regularly (with PhD's from schools in the US), have been giving me a resounding warning about applying to schools that clearly do not want and will never admit me because of the school's unpopularity and country of origin. One particular professor told me that Bachelor's degrees from this part of the world are not at all trusted and treated with disdain. I know lot's of schools encourage everybody to apply, but the exchange rates are not friendly, and I don't want to burn the scarce resources I have
QUESTIONS
1. Does country of undergraduate study matter to the graduate admissions committee?
2. Do schools in the US give off hints that applicants from certain backgrounds need not apply?
3. With the difference in educational standards, do I stand a chance at all, even if i find a school willing to admit me?
At least in my department/school in the U.S., we have several individuals from African countries studying for doctoral degrees. I'm a little concerned that there seems to be a disconnect between what you say about your performance (above average) and what your professors are saying (no one would want someone like you, possibly because of where you studied). 

As far as I can tell, most schools in the U.S. encourage individuals from diverse backgrounds to apply for their programs, including graduate school. So, I would not make a blanket statement that your country of origin and/or background is an immediate disqualification. 

Regarding your academic background, even U.S. colleges differ in terms of academic programs and rigor. That is why the graduate school admissions process involves many different parts, including standardized test scores, interviews, and/or letters of recommendation, that help the admissions committee get a more complete picture of you and how you may fit within the program.