Whenever an opponent searches his or her library, that player sacrifices a creature and loses 10 life.

Search your library for an instant card with converted mana cost 3, reveal it, and put it into your hand. Then repeat this process for instant cards with converted mana costs 2 and 1. Then shuffle your library.

Will Firemind's Foresight trigger Ob Nixilis once or thrice?

Thrice.

Firemind's Foresight has its controller search his or her library three separate times, and that will therefore trigger the opponent's Ob Nixilis, Unshackled three times.