Hi
@gazdgazd11 I completely empathize with being stressed about written exercises, as I also did not get to do a mock one before my ACs last year. However, I have found that in practice, as long as I could keep myself focused on being very-time efficient, they were not as challenging as I thought.
As for your question about types of written exercises, firstly, there's a variety of different 'email-based' formats - mostly in which a partner/associate asks you to complete a task and you need to respond and complete it on an email. Those include in many cases client letters/memos, but can also include some substantive legal analysis tasks (but where you are given all the legal resources you need) and administrative tasks such as proofreadings and scheduling tasks. Besides these, I have also seen article-based written tasks, which tend to be longer and be more argumentative (and in many ways more alike a university essay).
I do not think you always need an executive summary, and particularly if the answer is quite short or not overly complex. The point of the executive summary is to make your answer more readable by summarizing it at the very beginning. I think you should simply make a judgement call on the day on whether that is necessary or beneficial to include.