Wood stain is abosorbed into the wood, so the wood takes on the color of the stain. This is why the features of the wood are still visible, unlike with paint.
Depending on what the wood is and how it has been processed, there may be a semi finished surface on it. Sanding lightly will open the pores and allow the stain to absorb more evenly. Will also...
Yes you can use wood stain on concrete but it will not penetrate the concrete, it does look nice and you can use different shades together. To keep the stain on it use a concrete sealer in a couple...
Depends on the type of stain and wood. I would recommend you sand the original stain off (this should take 5 - 10 mins with a power sander and some 120 or 240 grit paper) then wipe clean with a cloth...