First let me answer to your questions.
Q:1 Does Team Pulse capture "acceptance criteria" in the "Given [context] and When [event] Then [outcome]" format? (or other format?)
At the moment acceptance criteria has title and description. In the description we added text template in the Given When Then format.
Q2: How does the Task or Story get linked to the "acceptance criteria" (the definition of "done") and then how does the acceptance criterion get linked to the Test? (the automation test recorded by Telerik Test Studio).
Acceptance Criteria are part of a story in TeamPulse. TestStudio has an integration with TeamPulse and they can associate test with acceptance criteria. You can learn more about the integration from the video
We are looking how to improve the integration between the two tools and to make TeamPulse more test friendly. Any suggestion and ideas that you have are welcome.
the Telerik team