1

Let's assume I have black card with "player must exile a creature" and one of mine opponents have only one creature on the battlefield, but it has "protection from black".

Does mine card affect his?

2

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.

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