How should a graduate student email a professor from another country in order to get feedback on their work?
Most professors, particularly well-known ones, get tons of such requests. And silently drop them into their recycle bin. They are busy people, with too much on their plates already, to go reviewing stuff that doesn't do them any good (reviewing a paper for a conference/journal, or a thesis, is part of their work, and not to be avoided; this is just work for nothing).

Get somebody in your environment to check over your work, they will tell you if it is any good, help you polish it and present it to where it will be looked at.