1. I don't think publications or conference presentations are particularly meaningful. Having a great writing sample that demonstrates your ability to do sociology is important, but folks generally don't care whether it was presented or not.
2. GRE scores, along with GPA, writing sample, statement and letters of recommendation, are important. Which factor is most important likely varies by department and individual. Good scores can probably help a mediocre GPA, but they won't compensate on any of the other factors. Bad scores can doom an application. In particular, if you can't do math, you probably aren't going to do well in graduate stats sequence.
3. We don't judge non-US applicants any differently. For folks who did not do their undergrad at an English speaking institution, we generally like to see some additional evidence that the applicant will feel comfortable writing and speaking English.