How do I redo and old set of rounded outside cement steps for inside?

I think you could remove the tile and use a sheet vinyl that you could cut to fit the curve of the stairs. You could make a paper pattern for the initial cutting--making just a bit bigger--and then trim the vinyl once you have it glued down. I see there is trim around the edges of your stair curves and someone very patiently made cuts so that it would fit. Maybe you can carefully remove that trim and reuse it or use it as a pattern to make new.

I like it, I would get a small tool to grind the loose concrete off and loose grout, then skim coat it with concrete and replace any missing grout. You could also use a wire brush on a drill, be sure to wear good goggles and gloves, long sleeved shirt. Wet the concrete before skimming with new concrete, and add a bit of white glue to the mix. Looks like just the bottom step needs work. Anything you do to the concrete will need annual maintenance.

I am guessing you used the wrong tile and adhesive. First, remove all the tiles. You say this is "indoors", but is the room "climate controlled", (protected from cold and heat), or just an enclosed porch? They make a bag mix of mortar, called "flex bond" sold at all Lowe's and Home Depot stores. The good news is Home Depot has free clinics for tile where they can teach you how to do this. Since it is live, after watching and listening to the instructor, you can ask any questions. This will hold up to extreme weather changes, and vibration, expansion and contraction, (which the concrete is always doing). #2. If it is in an area that gets cold, "ceramic tile" will NOT WORK! The tile must either be "Porcelain" or "quarry tile". Otherwise they will come off.

We cleaned ours built out the curve to square it and covered it w / plywood..then wood flooring