Translation:What is the next project?
What about "event" (as in "sporting event")? Would that require a clarifying modifier, or is it a valid translation of 项目?
including 一 feels clumsy, is it required? I generally use 下个 for next and 上个 for previous.
No, its actually colloquial to use 下个项目 instead of 下一个项目 since as a 量词, it should be 一个项目.