If your removing the tile it doesn't matter what it is doing or not doing. I would recommend a good solid surface/base under your new tile. Don't do spacing of your new tike like the existing. 1/4" is a good gap. The grout line along your tub base should be caulked with caulking the same color after grouting. Tubs are sometimes flexible at their base which isn't a kind environment for grout. The rust you speak of just might be mineral stain left behind from water getting out of the tub.