How do lone electrons impact the charge of an ion?
The two red dots indicate the presence of two electrons, not the absence, if there were no electrons there it would be balanced. The colours of the electrons in the image indicate their origin: blue electrons originate with oxygen, black from sulfur and red from an outside source (eg. Potassium or H2).
Ions have a charge because they have more or fewer electrons than the number of available protons. Sulfate has gained two extra electrons.
The arrows in the second image indicate a 'dative covalent bond' where the electrons in the covalent bond all come from one atom rather than being shared, while the lines indicate a normal covalent bond (ie. an electron from each atom. The extra electrons added to the oxygen atoms to form a full orbital level in the normal covalent bond are responsible for the extra charge.

There's a nice visual depiction here: http://chem-net.blogspot.co.uk/2013/02/electron-dot-structure-of-sulfate-ion.html