Do black spots remove all/most collector value? When there are black spots on a 1983 double die is it still valuable collector item? What are the lines to the left of the R and U that extend to the head on the obverse?
Black spots effect numismatic value just like fingerprints do. Anything mid 1982 on are zinc cored and most develop black spots and/or blisters that will eventually eat your cent with no ability to prevent it. Sucks for collectors, but there is nothing you can do. Luckily it's a very slow process.
Not certain what your lines atop Abe's head are for certain. Perhaps linear gas bubbles? Are they hollow? Try depressing them with a wooden toothpick to see if they are hollow. These began as a slight tear in the copper plating and over time expand. Are they raised or incuse? Could be a scratch.
Like fingerprints, they cannot be removed. The chemical composition is usually an inorganic insoluble complex of copper sulfide and oxide compounds. Like fingerprints, they are really a very shallow form of localized corrosion.
They are a problem, but in mild cases, do not completely diminish the value of the coin. The remaining value is very much subjective in the mind of a buyer.