OK that helps me, but whether I can help you is still uncertain... I do think that building on the slab is good in this case as it will spare you having to do a firm base of crushed gravel etc for the wall. BUT in using the slab as your base you are assuming that the slab is well supported and won't crack under the weight. Can you check this assumption? If you can't, perhaps the best place for the kids' sandbox is not beside this wall. Also, if you loved playing with bricks you will remember the concept of linking the walls across the corner, or into the corner towers in this case, with connector bricks? Sounds like a fun project; depending on whether you get any other input here (esp from people familiar with your climate) maybe read up a bit on wall design to ensure that your design is stable, and look for local info on the subject to make it good in your climate.

Pics before we did our updates:

I was just going to comment that you need at least 2 more panels on each side of the curtain rod. Drapes should drape when closed not look flat like a sheet thrown over a rod. The rod at both ends should be covered when the drapes are closed. No naked rod on the ends. I'm actually a little confused as to why you have shutters on one wall and on the adjoining wall there are curtains. A little color in the drapes would add life to the room.

I think you're giving the taper too much power. If something needs to be in a bin, that bin doesn't need to exactly fill up the whole shelf. Lots of stuff may not need to go in bins or baskets anyway. You could get 12"-deep boxes and put them on the deeper side, and leave the rest of the shelf for setting things that don't go in bins or boxes. Or, if you do need a bin that exactly fills the shelf, can't you use your plethora of woodworking tools to make your own in a trapezoidal shape? It's just an oddly shaped wooden drawer, which is itself a lidless wooden box. (I made a storage box/bin for an oddly shaped space by cutting up foam-core board and hot-gluing it together. Now and then I have to reinforce it, but it works great! I'm too lazy to make it out of wood, and I don't have a lot of experience using thinner wood like 1/4" luan or masonite, and 3/4" stock would be too heavy) You could install shelves, or you could make "pockets" to hang on the wall based on what's going to go in them (if you make your own pockets, you can make them as fat as you need for whatever you're going to put in them). I'd say: First, figure out how to put a single hanging rod on the 24"-deep side (and limit how many coats can go in there--everybody in the family gets two hangers, and any other outerwear goes in the bedroom). Or, put in one hanging rod (those Closet-Maid/Elfa wire shelves?) for long coats, and install second one halfway down the wall to convert one half of that space for jackets? My experience is that especially in winter, there are more hip-length coats than short jackets, so plan for winter, not spring or fall. Then see what sorts of other storage needs you can fulfill there--would the vacuum bit on the coats side? Can you put pockets on the side wall for gloves, hooks for umbrellas and dog leashes? Can you put a tray or basket on the floor to hold boots or shoes? Or something on the shelf above the hanging rod that would be useful for what you store there? Then stand in front of that tapered side with all the stuff you're going to put in there, and see what inspires you. Do you want shelves you can put boxes on? (You could make a small trapezoidal bookcase and bolt it to the wall, leaving space below it; or use brackets on the back wall to install tapered shelves--you can buy brackets of varying lengths.) Would pockets or baskets on the side wall be useful for stuff like cleaning supplies or shoes? Would hooks allow you to use the most shallow section for hanging the vacuum hose?