1)
a. Records and displays what an Admin has done recently? So that another Admin is not waisting time doing or checking if its been do.
There is an admin activity log created for security reasons but this is not really what you want.
(Admin Access management->Admin Activity logs)

2)
b. Something in the Admin side where Admins can add 'tasks that need to be completed'. Adding products/new suppliers/ ext ext ext?
If you mean a TODO list that shows at the top of the screen, yes: Admin Notes.
http://www.zen-cart.com/downloads.php?do=file&id=847

You could create a TODO note that displays when the job is pending, then when that task is completed, disable it so it does not display but the note can still be accessed for reference about that task as you require in point 1).

Shortly I'm about to upload a modified version of that plugin, contact me by pm if you want to try it first.