It's awesome that you're planning ahead for your cruise with your sister! I totally get wanting to make sure everything's sorted early, especially with her needing a routine.
1. Taking a powerboard sounds smart, especially with all the devices. I think your USB plug should cover everything, but it's good to have a backup plan.
2. For learning about Melanesian culture in Noumea, besides the cultural center, you might consider checking out local markets or any cultural events happening during your visit. Snorkeling at Signal Island sounds like a blast!
3. Sundays can be tricky for sure. While some places might open for cruise visitors, it's best to check with your cruise line or contact the places you're interested in. The duty-free store should be open, but it's always good to confirm if they'll sell alcohol on Sundays.
4. The cruise ship should store any alcohol you purchase in New Caledonia, even if it's not from the duty-free store, until you return to Sydney.