Salinity does affect your skimming. Protein skimming is possible with saltwater due to the higher viscosity of the water - which is why the don't work for freshwater. The higher the salinity, the better the skimming efficiency, but the most commonly encountered range for saltwater aquaria - 1.020 - 1.025, will all work fine with a negligable impact in performance from one end of that range to the other.
Does it affect clarity? ... personally, I think that saltwater tanks on average look clearer than freshwater, but that may just be my impression.
Any changes to salinity should be done slowly, unless you are dropping salinity in a QT for hyposalinity treatment, which follows different rules. If you are adjusting the salinity in your main tank, it should be done as slowly as possible unless you are dangerously low and your livestock has started to become affected by it. To raise salinity in a tank, use seawater for topoffs until it is where you want it. To drop it, change small amounts (5% or so) of tankwater for RO water every day or two until it is where you want it. In most cases the hobbyists discovers salinity issues by occasional tests of the water, and not due to obvious livestock issues. In those cases, there is no compelling reason to do it quickly, and the change, even though it's in a beneficial direction, can be more harmful to the livestock than the original problem, so it's best to err on the side of slow.
