>>is there a way to have a person removed from or put on to another list in iContact or Aweber once they subscribe to a product in DAP? Also, if they discontinue the subscription in DAP is there a way to have them put onto a list either in iContact or Aweber... all automatically <<

1) Upgrade
You can set up a product chaining rule in dap that says when a user is added to product B, automatically remove them from product A in dap.

Setup a rule directly in aweber that does the same thing - when a user is added to list B in aweber, remove from list A.

Now as long as you have integrated dap product A -> aweber list A, and dap product B -> aweber list B, the users will be in the right lists.
They do have to double-opt-in again to the new aweber list though.

2) Downgrade
When a user discontinues their dap subscription, aweber does not get notified.

The users lose access in dap automatically at the end of their current subscription cycle because the access end date will expire.

You can use product chaining to downgrade them in dap (when a user loses access to product B, set chaining rule to automatically give them access to product A and set up product A to add user to list A in aweber).

But the chaining rule will only be triggered if you manually click on 'Remove' under 'Product Access' in dap manage users page.

Set up filter rules in Aweber to remove user from list B when they get access to list A.