Can a nuke melt your eyes?

Answer 1

Literally, no. A "nuke" refers to a nuclear weapon or device. While it may have the potential to detonate or be detonated, by itself, it is largely inert, aside from a small amount of radioactive leakage, and in the case of liquid fueled missile engines a bit corrosive.

The detonation of a nuclear device can certainly produce the heat to instantly vaporize your whole body (A thermo-nuclear detonation--such as produced by a hydrogen bomb--produces temperatures that peak at 350 MK [million Kelvin]; that of a regular fission device peaks at 50 to 100 MK).

Further from the point of detonation, the heat falls off to that necessary to melt flesh. This is typically the zone of flash fires that the blast is not able to extinguish.

Still further out, it is still hot enough to flash burn the skin.

And even at distances of a hundred miles or more, the light energy is intense enough to produce flash blindness in those who faced the fireball.

To get a better idea of this, consider a very real scenario that was considered during the cold war. US expectations were that the Soviets had at any one time a device as large as 5 megatons pointed at the city of Grand Rapids, Michigan. At the center of Grand Rapids is a sculpture made by artist Alexander Calder, known locally simply as "The Calder." If the device detonated square on The Calder, the blast crater would be a half mile deep and extend from the south end of Riverside park to the north to Dickinson St SW to the south and from near the end of Lionsdale Dr. NE to Edison Park Ave. NW. That's roughly five times the size of meteor crater in Arizona. This is the ring of vaporization. Everything would be flattened from there to Lake Michigan in the West, south of Wayland in the South, past Ionia to the East, and Howard City in the North. This is the ring of melting flesh. Heat would be felt from the center of Lake Michigan in the West, Owosso in the East, ten miles north of Reed City, and Constantine in the south.