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The default project type in OF is a sequential one, i.e. the tasks in it are meant to be completed in order. That's why setting the due date for the last task makes no difference to whether the task appears in context view or not. You can change it to a parallel project if you want to be able to move on all the tasks in the project simultaneously i.e. have them all appear as available actions in context view.

Have a look through the mini-manual, IIRC it explains how to switch between these two project types. Also, if you're not familiar with it, try reading a bit about Getting Things Done e.g. at 43folders.com: it's the system on which OF is largely based.