We just got back from our first trip! (At least, first for me and the girls, and my wife hand't been in 30-some yrs.) I'd reiterate the advice to not freak out.* But if you're like me, you're enjoying the planning and looking for hard data, so here are some thoughts!
It might be impossible, but I'd encourage you to make every effort to FP FoP (even though you have one on your last day) and RD Navi River. Navi seems to almost always be a very easy RD (we waited 30' when arriving 10' after start of EMH; if we'd been earlier it would have been walk-on), and FoP even at RD seems to be an arduous multi-hour experience. You'd lose the chance to do other things with your time and start the day with a tense and unpleasant ordeal. But if you can't get the FP, then never mind I said that!! it will be great. And it's true you'll want to do FoP more than once—IMO the best ride in Disney World right now. We started our trip with it, and it was a truly magical thing to do first.
I heartily support lunch at Tusker, though
I would warn to show up early for ROL or your prioritized seating might be gone.
I also heartily support the afternoon breaks. We actually only went back to our resort two days, once to nap and explore the resort and pool, and once to change into full-on princess cosplay with wigs and all. We're paying enough for hotel amenities that it's nice to enjoy them. But even if you're feeling better than you thought and want to ride out the afternoon in park, take the pace easy and use it to check out some of the more restful activities—explore Tom Sawyer's Island, do the Gorilla or Maharajah trails, sit and marvel at an EPCOT pavilion.
Philosophical sidebar: This is about what makes Disney different from other theme parks. If the point is to race from roller coaster to roller coaster, then for one thing there are places with bigger and scarier coasters, and for another you'll be run off your feet. The point of Disney is "Imagineering," which means immersive detail. It's to spend time saying "Oh look at that, I can't believe they thought of that." The inlaid murals under Cinderella's castle, the fake layer of dust on the cooling pipes running through the FoP queue. Everybody, I'm sure, has their own style of "doing Disney" and their own pace, but for us, especially for a first trip, we needed a pace that let us explore, marvel, and rest, even in the parks. That often meant that each FP actually took the hour allotted to it, what with getting there, getting through the gift shop, and getting to the next thing with a bathroom break on the way. All that is to say, maybe a trip back to the hotel in the afternoon will be needed for that restful experience, but maybe it will put enough pressure on the remainder of the day that it's a net loss. Don't be afraid to decide on the fly—or to put the 6-yr-old in a stroller (or Mom or Dad in a wheelchair!).
Buzz was a very fun ride and I'm glad we did it. It's exactly the sort of ride, though, that you can often snag a "4th FP" for, and wait times are usually under an hour anyway. You might try to poach a Space Mtn FP out of it instead (unless your party isn't that into coasters. It was my eldest's favorite ride at WDW!). (By the way, if you haven't read
https://www.mousehacking.com/blog/disney-world-fastpass-strategy yet, especially the stuff at the bottom about "tap & grab," do so. I found that the notion that you could modify a high-demand FP to an earlier time was unlikely—no, you can't budge your FoP's time even day-of, though I was surprised to score Tower of Terror and even Slinky Dog as post-3rd FPs. But most of all, don't despair if the FPs you got weren't exactly what you wanted; keep checking especially in this first week after FP day; I saw some movement.)
That depends a lot on how your party feels about character meetings. One of my daughters was absolutely freaked out by these big-headed monsters and by personal attention, and the other could take it or leave it. I'd point out that you'll meet (probably) Mickey, Goofy, & Daisy at Tusker House. We also rounded out our character quota easily with Snow White, Dopey, Grumpy, and THE EVIL QUEEN at Storybook Dining w Snow White, and the whole star-studded cast at Cinderella's Royal Table.
Personally I wouldn't burn a FP or more than 30' in line on a character meeting on my first trip, but that's just my priorities. I notice your plan doesn't include Seven Dwarfs Mine Train. Maybe you couldn't snag the FP (and maybe you won't be able to), but if you could that's what I'd put there. Don't get me wrong, it's not
that awesome, and I wouldn't stand in line 4 hours for it, but it strikes the perfect balance of "cute dark ride" with "mildly thrilling coaster." Your first day has Early Morning Magic, which I found the most painless way of getting access to 7DMT plus Peter Pan et al. It would be quite a chunk of change for 5, but
I didn't regret it. (Granted, I only had two "Disney adults"!)
Well, don't skip seeing the show, for sure! Believe the hype—acrobats, fire jugglers, aerialists, great singers. (Also, we did the Nemo musical which I'd heard poo-poohed, perhaps because it's not as awesome as Lion King. But it was also well worth catching; if there were no Lion King everyone would be singing the praises of Nemo. Two very different approaches.) But it's true that shows can be a "waste" of a Fastpass. They don't usually get you any better seating and it doesn't (significantly) affect your wait; everybody has to wait until the previous show finishes. The catch is that you wait in a shorter line, and this is a popular show. We showed up maybe 20' before show time and only
barely got in, taking some of the last seats in the theater. You do
not want to miss getting in and have to wait until the next one. But yeah, for Indy in particular and shows in general my advice would be "Don't waste the FP, show up 30' early, and aim for a less-popular show time,"
UNLESS it's a very high-traffic day. I'm no expert but in June you ought to be lower traffic than our Spring Break experience. So maybe, if your family are coaster lovers, you want to turn this into a second Everest?
* One point of view that helped us keep things in perspective was the question, "What would it take to 'ruin the trip?'" It's conceivable—a hurricane shuts down FL, somebody breaks a leg, etc. But missing a FP, a ride being down, a rude CM—these things don't have to "ruin" the day or the trip. Let them be disappointments, but don't let them overcloud the experience.
