The second ability has an “intervening ‘if’ clause.” That means (1) the ability won’t trigger at all unless, as an opponent’s upkeep starts, that player has no cards in hand and Quest for the Nihil Stone has two or more quest counters on it, and (2) the ability will do nothing if that player has at least one card in hand and/or Quest for the Nihil Stone has fewer than two quest counters on it by the time it resolves. (If Quest for the Nihil Stone is no longer on the battlefield by that point, its last existence on the battlefield is checked to see how many quest counters were on it.)