Not sure I can answer all your questions -but I'll try!
The fridges are regular resort-sized - same as WDW deluxes. Actually I thought they were bigger but I'm sure they're just the standard ones you'd see in any hotel on or off property.
Yes there is a refillable mug just for S/D. It's really nice - looks like an insultaed coffee travel mug- the one I saw at Picabu 2 weeks ago anyway. There may be other styles that I didn't see. I wish I would have gotten one but literally had no room to pack it to take home! I don't know the price, sorry.
That area is GREAT for non-resort activity. There is Fantasia Gardens mini golf within walking distance (across from The Swan), and The Boardwalk itself offers a lot to do - shopping, eating, watching the street performers, renting bikes, etc. You can also walk to YC & BC for alternative dining. The Dolphin has an arcade if your kids are into that (and it's aside of the laundry room if you need to get a quick load in while they're playing!) The candy store in The Dolphin is an activity in itself, my kids can spend half an hour in there.
I don't think the Grotto Pool has zero entry, someone correct me if I'm wrong. When we were there 2 weeks ago it was chilly & there was no lifeguard, the sign at the waterslide said to use at your own risk. So you could have gone down with your child, but I'm not sure what the actual rule is if there is a lifeguard there watching. There is a pool shack with all kinds of equipment - didn't specifically see life jackets, but I wasn't looking for them.
As far as Illuminations - this is my favorite fireworks show ever. It makes me cry every time! That being said, however, you have to be right there inside Epcot to fully see it. It's a show - including fireworks, that tells the story of humanity. You are correct, there are no high fireworks for a few minutes during Illuminations - at this point there is a barge that has a globe in the middle of the lagoon, that can only be seen from inside the park. This is the story-telling part of the show. Honestly I don't even care to watch Illumination if I can't see the whole thing or hear the music, that is what makes the show so moving. But yes, you can see the highest fireworks from an Epcot Fireworks View Room - here is a shot from 2 weeks ago from that category room:
Would I pay for that category room? Honestly, no. You can see the same view of Illuminations from The Boardwalk area. If you have park hoppers it's well worth it just to walk (or boat) over to Epcot to watch Illuminations from inside the park. I did this twice on our last trip - ran over for 45 min. & headed back. But if that's important to you, then go for it!