[Arran]

 Try using Mohawk or Deft tone spray on the carved piece, probably a light or medium walnut, the wood probably needed to be sealed first with sanding sealer. The top is also walnut, French walnut veneer by the looks of things. You will probably have to experiment with some chemicals to get the stains out, either phosphoric acid or oxalic acid. Phosphoric acid will remove iron stains, you put it on the stained area, wait until  they fade, then wipe it off with a damp rag or paper towel and then dry it off. Oxalic acid is often used as a wood bleach and I have had no experience with it. 
Regards
Arran