Ok, lots of questions!
Firstly, to my knowledge it’s always a partner that interviews you; certainly that has been the case for everybody I’ve spoken to at the post-offer events.
The written exercise is really quite simple. On the Deloitte website there is a section which gives you a basic outline of the company you’ll be using, and when you start the e-tray section you’ll be given more information which you’ll have to read and then refer back to. That’s all the information you’ll be given and it’s all you need, though of course some understanding of the wider commercial environment won’t do you any harm. You can’t revise for or prepare the ‘presentation’ (which in my case was just a short conversation anyway), it’s just a short explanation of your reasoning.
As for the interview itself… you should look at their core competencies listed on the website, have at least two stories prepped for each, and think about how those stories would be beneficial in business environment. Your interviewer may go off topic following one of your answers so it’s best to have thought around the story, rather than simply learning it by rote. Commercial awareness tends to be tested by ‘tell me about an issue you think is affecting [your service line/team/group] at the moment’. Pick a couple of things from the week preceding your a/c, and then research around them and try to link it back to both the business and your own experience.
Hope that helps, let me know if there’s anything else.