Do indiviuals with a E-2 Visa have any taxes, state, city, federal or Social Security taxes deducted from their payroll check?

The "E" visa is considered to be a work visa, so, yes, you will pay all the same taxes that a U.S. citizen will pay, to include the FICA (Social Security and Medicare) taxes, even though it is likely you will NOT qualify for any benefits under these programs.

It is NOT fair, but NO ONE has EVER said the U.S. tax system is fair!