Black card ability - all players exile a creature - does it work on the one with protection from black
Yes, it does. Your card does not target the creature, so its protection ability does not help here.
Remember that protection can be summarized with the mnemonic acronym DEBT:

The object with protection cannot be:

Damaged by sources with the specified quality. (All such damage is prevented.)
Enchanted or equipped by permanents with the specified quality.
Blocked by creatures with the specified quality.
Targeted by spells with the specified quality, or by abilities from sources of that quality.


Your card might target the player but it'll never target the creature directly.