How can I update a particular activity/case via a webform?
You could create a View of Webform Submissions.  It's a bit more complicated, but you should be able to achieve it (if I understand you correctly).

Be sure to add the web form submission data (I think that's the one) relationship so you can sort and filter.

Additional thoughts:
I'm trying to get away from views of webform submissions as they are not fun to create/maintain.

Another alternative, and the way I tend to go now, is to create a View of CiviCRM Relationships with the current user in the contextual filter.  Include the contact id, case id and activity id fields in the view, but exclude them from the display.  Add Case Types and other pertinent info to the view to help distinguish each case and a global text field(s) that links to a new webform.

Create the new webform by cloning the original, on the CiviCRM integration tab change the case section to update existing case and/or activity.

Where your scenario gets tricky for me to understand, is the activity and the case together in one webform.  You may need to separate these into two new webforms.  One that updates a case and one that updates an activity and create two links in the view one like:node/new_webform_id?cid1=[id]&amp;aid=[id_1] to update the activityand one like:node/new_webform_id?cid1=[id]&amp;caseid=[id_2] to update the case.