1. Rock Harbor.
2. As long as possible . From Rock Harbor, #1 would be to do the 4 mile round trip trail to Scoville Point. You can also rent canoes and kayaks. #2 would be to paddle to Hidden Lake (a couple miles) and hike up to Lookout Louise (a mile or so up). At Windigo, there's a couple out out and back hikes, and renting canoes/kayaks.
3. Yes, in Rock Harbor only. Contact the Rock Harbor Lodge: https://www.rockharborlodge.com/sightseeing-schedule. Although I would verify they're doing the boat tours this year (because of Covid-19). #3 would be to do the Edison Fishery/Lighthouse tour, if it's the right day and plane reservations allow--but it takes the better part of a day.
4. Rock Harbor has a restaurant and grill. Windigo has a store and snacks. But since you'll probably be out and about, you may want to bring your own.
Remember you're on island time, and schedules are best estimates. Weather often influences them, especially the seaplane. Not uncommon to be delayed, and in some cases you could be asked to leave early. But would be a very nice day trip that will make you want to come back and stay longer!
To Ingo's point about the weather influencing the seaplane, it's also possible that the return trip may be delayed and you could spend the night on the island. Personally, I'd try to be prepared for that event too.
If you're coming from the MN side, another option would be to head over to Windigo on the Sea Hunter III. It's not as dependent on weather as flying.
That would give you about 4 hours on the island.
