Comparing Polarity of Amino Acids
Does the charge on the acidic and basic amino acids make them more polar and hydrophilic than the uncharged polar amino acids? 


Yes, they are less likely to be on the inside of a protein. Hydrogen bonds with water will be stronger, and interactions with ions as well.


  Moreover, cysteine is classified as an uncharged amino acid, but because it has an ionizable side chain, would it be more polar than serine, asparagine, etc.?


Cysteine and tyrosine are more hydrophilic when deprotonated. So at strongly basic pH, their properties are very different from that of serine. At neutral pH, however, cysteine is less polar than serine.