I would like for a task to appear in multiple projects - is it possible to do this and if so, how do I do so?
Unfortunately, that's not possible. Every task in Todoist can only belong to one project, but there are other task properties that multiple tasks have in common. Aside from the obvious ones - date and priority, you could use labels. One task can have multiple labels and you can also search for labels or access them from the left pane, just like projects.
In fact, unlike projects, you can even include or exclude labels from search results and see tasks that are due "today & @home" or "10 days & !@work".