Disclaimer: I don't know you, your personality, or work ethic so please don't think I'm trying to be condescending or think you don't understand basic social norms, I'm just trying to cover all the bases and make sure you don't slip up like I have or have seen others do in the past.
It's a little hard for me to say not knowing the full situation but given you are friends/friendly with this CEO some level of constructive criticism or inefficiencies that you see. It's important to temper that advice and make sure if come across as "here is what I saw" and not "here is what you are doing wrong". Remember, your advice might not be new and they may have already attempted or researched some of your ideas and found them lacking. Just don't go in with a know-it-all attitude, be gracious and potentially hold back any criticisms until asked.
Also I would make a point to write down and convey to the CEO things you see that are being done right/efficiently. This will help balance out any issues you report and, to be brutally honest, make the CEO feel better about letting you shadow them. You don't have to brown nose but don't be a negative Nancy either.
It's going to be hard to for me to give you "useful topics/notes that I should track of to include in a report" because I just don't know that industry and frankly if I were in your shoes I would just go in with a blank slate and record everything I saw/heard of note then try to reflect on what I've recorded at the end of the day instead of looking for specific things.
Best of luck to you and I hope it goes well. I'd love a followup (not with any specific details necessarily) about how it goes!
