To remove darks rings, stains or gray oxidation, you will need to use some oxalic acid crystals . It is the main ingredient in the so called deck brighteners. To use them, you have to mix them with warm water until you reach a saturated solution meaning it won't dissolve anymore. Only mix the amount you need. You will need to apply it with a synthetic brush giving the entire surface a good wet coat (not just the stain) . The wood will need to be bare and lightly sanded prior to this step. Make sure you apply it to the whole surface and not just the spot. Leave the acid on until it dries or until the stain has vanished. Follow that with a couple washes of water to remove the residue. The grain will be raised after it dries, so you will need to sand it smooth before finishing. Make sure you use a particle mask when sanding because what crystals are left over will make you sneeze if you inhale them. Do it outdoors if possible. 

If some melted wax gets on your table top, hopefully it hasn't hurt the finish. Since you just cant wipe it off with a damp cloth, you have to scrape it off. Yes it sounds scary, but it isn't really. The scraping tool of choice would be an ordinary credit card. You shouldn't try to scrape it all off at once, but by taking it off in thin layers, it will eventually come off. Since the card is softer than the finish, (We Hope), is doesn't scratch the surface. Once you get as much off as you can, you can then remove the remaining wax with a soft cloth dipped in lemon oil.