Yes, you can repair areas of the flooring yourself. The major problem in your case will be to remove the stains. Suggest sanding down to the bare wood and try stain removers. May have to resort to bleach solution? When satisfied, remove any stain remover and let dry very well. Then apply the same type finish with a good brush. May have to sand again several times with fine sandpaper. The last coat of finish will depend on the type finish (gloss, semi gloss or satin). Satin is the best to match. I use a clean rag to apply the last coat and it blends in fine with the rest of the floor.