How large is Joachim & Marie's home???
You can see by the side aerial view in the previous post that it is a fair size, with nice, large public rooms and with two symmetrical wings, there is probably a family wing and a guest wing. The third or attic level would traditionally house staff. Who knows how many live-in staff they have - or not.
I have never seen pictures/articles on how many family bedrooms, and how many guest suites they have, and what the various rooms are . Any information will be appreciated. Especially pictures (if available).
You'll never find this information. It's just not public.
What about the Gatehouse (where Alex's parents lived for a number of years)

Take a look at the side aerial photo (where you can see the trampoline at the bottom of the photo). The gate house is just off to the side of the wing of the house that is opposite the one with the trampoline in the side yard. It's a bit in the trees. It was off to the side enough to be private, but also close enough for easy visits. I have seen a better aerial shot that show it but I can't find it to post for you.
Does Schackenborg boast an indoor pool (in case they invite the Icon for a pool-BQ party)??
There is no pool, indoor or outdoor, at Schackenborg.