To filter tasks by start or due date range, click on the Filter button next to the search field and select either Start Date or Due Date in the dropdown. The secondary drop down menu will be labeled All to indicate all dates. To refine the dates, click on All to open a calendar pop-up, then first select the beginning and ending dates for the range. (For the range, the beginning date must be earlier than the ending date.)
Depending on a user's project permissions, they may be able to view all the project tasks or only a subset. Watchers specifically added to the task will be able to view it.