I don't like your plans at all. They make me sad.
What is the platform at the bottom for? It looks too small to place a stool on without fear of falling off. Standing up will also be a problem, as there is not enough room to stand.
You don't need a platform at all, ditch it, stand or sit on the perfectly good floor that is there.
Adjustable height table top will likely be rickety and overly complex. Ditch it and anchor the bench to the studs for rock solid stability.
The legs extending above the work surface...ditch them, especially the ones in the front. They diminish your already small work surface and won't be needed when the tabletop is fixed.
Mount a couple of sturdy shelves above the work surface for storage.
I would lag 2x4s to the sides and back of the alcove, cut a top from butcher block counter material or doubled up 3/4" plywood and screw it down. Dead simple, no legs, no base, no obstructions, cheap and easy.