ᐅ Children’s play area with sand and mud

Hello!
I want to create a children's play area in a former shrub bed, including a playhouse (which we already have, but without a floor), a sandbox, and a mud kitchen. Available materials are sandstone blocks and tree trunk pieces (I’d like to use these to build the sandbox border), as well as an old sink with a faucet.
What advice can you give me? Especially regarding the preparation of the ground? How deep should the sandbox be dug? What should be placed at the bottom to allow drainage but keep weeds out?
How would you prepare the ground for the playhouse?
Do you have any other nice ideas for this children’s play area?
So far, we have only cleared out the bed...
Thanks for any feedback and tips! :-)

We have a few centimeters of gravel, a weed barrier fabric (a very thick mat), then sand.

I would also plan for good coverage to prevent the cats from repurposing the playground.

Mine is open and, strangely, it is neither a toilet nor an ant nest.
Can you set up a sunshade so that it serves as a cover when not in use?

We excavated the sandbox to about 50 cm (20 inches) deep. There is no liner or anything else, so nothing grows up from below. This also allows the kids to dig quite deep. We cover it with a breathable sunshade sail measuring approximately 2 by 3 meters (6.5 by 10 feet). Rainwater simply drains through. We bought the wood cheaply from a local classifieds website.

Thank you very much, also for the pictures! I'm really looking forward to the new small construction site now, only the weather isn't cooperating completely. ;-)