Assigned Activites not showing up on users Contact Dashboard
Maybe over complicating things a lot here. But assuming you have confirmed this isn't possible directly via 'permissions' and the users Contact Dashboard, I would try the following in Drupal. Build an Activities based Views block which uses Contextual Filter and Views 'relationships' (to get the Activity assignee) which will show the user 'their Activities'. Assuming that gives you the list you want, then add a link to each Activity in the View that jumps them to a Webform-CiviCRM with the activity ID in the URL. That might be getting you close.