I am sure not an expert but will give you some things to try. Depending on how much adhesive is left, my first thought would be GooGone, available at most hardware stores. If this doesn't work, you might check the Citristrip website and see if they have specific suggestions, but I would try the GooGone and putty knife routine first.
Regarding the cracked tread, my suggestion would depend on what kind of wood it was. If pine and you are in a relatively new house, the builder probably meant for the stairs to be carpeted. I would use automotive Bondo and try to force it into the crack as much as possible with your trusty putty knife. Bondo smells and the fumes are not good for you, so do this when the windows are open. Since it is pink, the color match might not be too bad with pine or even maple, but it will not take stain. If your stairs are oak, use Minwax wood filler. It is close chemically to the Bondo and you use it the same way, but it does not smell nearly as bad and does take stain--sort of. Hope this helps, or at least gives you a direction to start.