Explain why these ions are more strongly hydrated in an aqueous solution?
I believe your reasoning is correct (more or less). Solvation is influenced by charge to size ratios. Higher the charge to size ratio, the easier it is for the species to be solvated by water molecules. 

Apply this idea to both your cases. (note: in the second case, I don't get your argument about molar mass. The idea is much simpler, magnesium's atomic radius is smaller than sodium's and it has a higher positive charge. What can we conclude from this?

Also, reconsider the first case: a positive ion would not be attracted to the positive end of a dipole.