What kind of taxes is a G4 visa holder exemption of? and how can that holder ask for return them?

A G-4 visa holder is exempt from ALL taxes on income earned in his primary job.

He MAY be liable for taxes on stock transactions, however; it depends on the tax treaty between the U.S. and his home country.

If the spouse of the primary G-4 visaholder gets permission to work and does so, that salary is fully taxable.