Wet concrete is VERY heavy.

Make sure you can support the weight until it develops enough strength to support itself.

Your description is unclear to me, but if it were me I'd handle the design and construction using a 4-inch reinforced floor PIP concrete slab over a waterproof membrane over insulation over 8-inches of compacted fill material. Around the perimeter I'd use a reinforced continuous stem footing to support the perimeter walls. For the walls I'd use 8-inch reinforced PIP concrete walls with a reinforced top concrete slab designed for the span that you will have. I'd also waterproof the outside face of the perimeter walls and backfill such that all surface water will drain positively away from the concrete walls. How will you enter the shelter--from inside your house or outside?

Please READ this! We just had this issue and the first pour of concrete had to be ripped out! We are having many issues with our builder and how he builds things and this was one of the worse. He constructed the framing incorrectly. Didn't follow engineered plans. So he had to use foam to avoid having 10" of concrete poured. The rebar ended up on the bottom of the poured concrete and not in the middle of the concrete. The foam only permitted the rebar to be pushed down into it. They had concrete chairs...but once they walked on it...it just pushed it into the foam. So you have to majorly have support underneath. If you use foam allow for a solid board to go on top then cover in plastic if you don't want anything to stick to concrete. But we had to have rebar 6" apart with wire mesh. We used water stop and flashing around edges first time (we he homeowners supplied it)...second time around we didn't thinking the builder would do it NOT...and it leaks!! So Yes get waterstop or atleast flash it!

This is a structure that must be designed by an engineer. An engineer would first need to know the dimensions between the foundation walls. He/she would then decide if the slab would be structural or if the slab would be supported by a substructure like metal decking or Pressure Treated wood framing.

Your solution would probably work if you held the wood framing back at the edges so only concrete was exposed to the outside. Anchor the turned down slab to the foundation wall as you would any other structure. Welded wire fabric might reduce slab cracking. Use a durable mix (air-entrainment, etc.)

For the waterproofing membrane I recommend Grace Ice & Water Shield (without substitution) self-adhered directly to the plywood with the overlapping joints rolled with a steel hand-roller (very important). Grace makes a water-based primer (WB Primer) that greatly increases the bond to porous materials (it is sold in 5 gal containers but a foundation contractor might have some). The insulation should be high-density extruded polystyrene mechanically fastened in place with concrete poured directly on it.

The size and spacing of the joists depends on the span, the weight of the concrete and the regional outdoor deck loading.

Provide adequate flashing at the wall of the house and any penetrations for posts and railings. The walls of the shelter should be waterproofed, drained and insulated as needed for your climate and site conditions.