Does a salt always have a neutral charge?
A salt is an ionic solid compound. As such, it needs to have a zero net charge.

However, that doesn't mean it should contain only one cation and one anion. The stoichiometry of the salt depends on the charges of the ions. For instance, iron (III) sulfate is $\ce{Fe2(SO4)3}$; this stoichiometry is required to balance the charges from $\ce{Fe^3+}$ and $\ce{SO4^2-}$. 

Also, other types of salt exist, called mixed salts. They contain several different cations and/or anions (e. g. $\ce{KAl(SO4)2}$). 

Compounds with a net charge exist, they are just not called salts (look up Complexes). 


  In relation, are acids and bases charged?


Acids may (e. g. $\ce{NH4+}$) or may not (e. g. $\ce{H2SO4}$) be charged. Similarly, bases may (e. g. $\ce{SO4^2-}$) or may not (e. g. $\ce{NH3}$) be charged.