Angol tanár could be understood either way - a teacher who happens to be English, or a (possibly Hungarian) teacher who teaches the English language. Amerikai tanár would almost certainly be understood as "a teacher who is American" since "American" isn't generally seen as the name of a subject you could teach.
Not in English. It simply is not said. If the sex needs to be commented on, "woman artist" would be used. However, usually the pronoun is enough. "She is a leading artist" clearly refers to a woman who is an artist. "She is a leading woman artist" means out of all women who are artists she is leading - but probably not in comparison to male artists.