Why isn't the ionic radius of Mg2+ bigger than F-?
These two species are isoelectronic (have the same number of electrons). In fact, they're electronically identical with the except that the magnesium ion has 3 more protons. Since all other electronic factors are equal, the net effect is that the three extra protons pull all of the electrons in closer to the nucleus. I think you understand this part.

Electronegativity is not correctly used in this context. One way to think about it is that you should only be using that concept on a neutral atom. The fact the fluoride anion is negative and magnesium cation is positive means you've already applied electronegativity to the system in order to ionize them.