Every Member of the Team (Including Me)
The Business Analyst, Product Owner, and Scrum Master should work together and do this and report the critical information to the team.
Agile Team Members
Agile Business Analyst
None, Agile doesn't requre documentation
As much as I can with as much detail as possible
Just enough to be considered reasonible based on the nature of the project
What ever the customer asked for in the acceptance criteria.
Here's an interesting quiz for you.