Actually, Mg2+ and Na+1 are the same molecule if you take a closer look at where they are situated in the periodic table. If Mg loses 2 electrons, it will have the same electron configuration as Neon (except for the extra 2 protons). This is also true of Na, however, the difference is that Mg has 1 more proton than Na does, so it has a more slightly positive charge. Now for O and Cl, well O2- obviously has 2 extra electrons, but Cl has only 1 extra electron so Oxygen carries a greater negative charge, and because it is situated higher on the periodic table, it's electronegative charge will be greater. So, you have a Mg ion that is more positively charged, and an oxygen that is more negatively charge so they have stronger attractions for each other.
For the second question, take the example that wiki gave you: Ca2+ is an ion whose s orbital will be empty, and you will be left with a full 3p orbital. That, compared to Hg, is not as polar because Hg2+ will lose 2 electrons in its d orbital and so 8 electrons will be left to occupy a d orbital. This lack of 2 electrons from a full d orbital, will mean that Hg is more likely to bond because it's not as stable as Ca2+ in its full p orbital. And note that Fajan's rule looks at whether something will bind covalently OR ionically, not just covalently because some atoms do not tend to form covalent bonds, depending on what the other atom is that they bind to.