I don't think I can help you on the full assignment within the scope of an AMA; especially since the sub-question reads like the company probably is going to be using this question for other candidates in the future. However, here are a few tips for any take-home interview round like this:
- If you're given the opportunity to ask follow-up questions, make sure you do so; one key part of the exercise is seeing how you learn and research.
- Make sure you do your homework; know what the current messaging, positioning, audience, and content available is.
- Spend the time to proofread and polish your content. It should sing, and show you know how to both write, edit, and (lightly) design.
- Know the "brand voice" of the company interviewing you, and stay within it.
- Edit, edit, edit. If someone asks for two pages, don't get them three. Brevity is hard, but very important.