One of the main points of fasting is to deprive the body of nutrients so not sure what you are asking. Also your title asks about nutrients while you only talk about vitamin/mineral supplements in your post body so not sure what are you really asking.
Personally I only take electrolytes, magnesium (which I take regardless of fasting or not) and my cholesterol medication when water fasting.
As for nutrients, you have enough nutrients stored in your body to last for over a month without any input so I wouldn’t worry about that aspect on a 72h fast.
I don’t know if most people even take supplements while fasting, since some are better consumed while eating. Omega-3 oils are one of them. You can consume vitamin B on an empty stomach, but some people can feel sick when doing so. If you have a deficiency and want to fast, it is better to talk to your doctor first.
As for the drinks, I don’t have much of an opinion on them. I usually stick to tea, and chamomile helps me sleep well, so I have no use for melatonin. I don’t know what kind of workouts you plan to do during your fast, but if this is your first 72-hour fast, I would take it easy. Your body is already working hard to adjust to 72 hours without food. It doesn’t need you to overwork yourself as well. 10 calories is negligible so long as you only stick to one drink.