I don't know how deep to make the foundations. I expect to hire some
sort of post hole borer and make the main structure supported by 3 in x
3in or 4in x 4in treated fence posts with load bearing horizontals

I have built something very similar.

advice:Use 4x4. A hole 60cm deep for the posts. Cut the joints in the
posts before you start. Use bags of post-mix in the holes. Buy a "post
level" a sort of two-way spirit level.

thoughts: have you considered that your fort may be a bit too planned.
With a 7 year old I would be tempted to build the frame and walls and let
him/her finish it off. Give the child a bag of nails a hammer and a few
planks, hey maybe even a tenon saw. I fear a generation is coming that
hasn't suffered a splinter.