I would not be concerned with the "algae" on the sand as that is quite normal and to be expected, I personaly would worry if it did not form as it is part of the natural biology and diversity of the tank. Such algae is a good food source for most of the sandbed's infauna (sand dwelling organisms).
Are you sure the crab was actualy dead and you were not seeing its shed (molt) exoskeleton? If your nitrate and phosphate test results warrant a water change, then by all means, do so. If not, then I would not be too concerned if all else is doing okay. You might consider a sea cucumber to help mop up some of that growth on the sandbed, but do try and get a smaller species if possible. If you can find this species, I have found them to be the best for aquarium use.
Charles