Does the F-16 have any armor at all?
No.  The aircraft in question do not have ballistic protection, though they do offer system redundancy for battle damage and have to meet certain survivability criteria in live fire tests during development.

Just a note:  the only armor an A10 carries is a titanium pressure vessel for a cockpit which can take the kind of ballistic punishment you described.  It’s main defense is system redundancy, self sealing fuel tanks and engines mounted well away from the airframe and fuel.

Again the chief reasons combat aircraft do not carry external ballistic armor is any kind of armor over the exterior which can deflect the kind of AP/HE/Frag type warheads used in AAA/AAM/SAM warheads would make the aircraft prohibitively heavy and drastically reduce the warload and performance metrics the airplane needs to survive in combat.  And fighters like the F-16 and F-22 are considerably more vulnerable to enemy fire with engine surrounded by fuel tanks, causing even properly placed small arms fire to be catastrophic.