1) I also graduated 2 years ago but I've been teaching English in South Korea so I'm hoping that doesn't put me at a disadvantage.
2) And yes they accept international students and pay for travel expenses. So you should be fine!
3) As for experience, I have a wide range of curatorial internships on my resume as well as in other departments (Development and Education) and I graduated with a degree in Art History. But since I'm fluent in Spanish (which is preferred for the internship I applied), I'm hoping that will make up for my lack of involvement in the art world these past two years...we'll see