All your suggestions seem fine to me. 'Academic papers' are usually written by career academics or doctoral students, rather than just any student. The word 'coursework' is commonly used in the UK to refer to assessable work done by 16-18 year-olds; so I think at University they talk about 'term papers', 'essays' or 'assignments'; 'coursework' is understandable, but regarded as a rather juvenile practice! A longer essay (but not a thesis) is called a 'dissertation'.
The Open University (an on-line/distance learning organization) has, apart from exams, two kinds of assignment: TMAs (tutor-marked) and CMAs (computer-marked).