From my personal experience,
Tasks do not inherit the milestone from the parent, just as User Stories do not inherit the milestone from the feature/portfolio item.
You can assign milestones to Tasks themselves. You can do this from the U.I. doing a bulk edit from a grid/list view (i.e. select more than one task, left click and select Milestone. The only caveat is you can't see the milestone box inside the task itself. You can only view or edit a task's milestone from the grid/list view.
You can set up a query to check task milestones against the workproducts' milestones, so it will tell you how many tasks are out of sync with their parents. You can change ALL the Milestones for all the stories and their tasks in a feature if you expand all the stories and select all and milestone. It might take a while and you might have to refresh to ensure it worked entirely (by adding milestones column to the grid). When expanding, you need to scroll through the entire list so all stories open up before triggering select all.
Hope this helps,
Michael Addington.