What is the interpretation of the phrase "بلغوا النكاح" (balaghū an-nikāḥ - reached the age of marriage) mentioned in the verse: "And test the orphans until they reach the age of marriage (an-nikāḥ). Then if you perceive in them sound judgment..."? And how does one respond to those who see a contradiction between it and His saying, exalted be He, "وَلِلَّائِي لَمْ يَحِضْنَ" (wal-lā'ī lam yaḥiḍna - and for those who have not yet menstruated)?

There is no contradiction between the two verses. The first verse (And test the orphans until they reach the age of marriage) speaks about the orphan's property and when it should be handed over to them. "Reach the age of marriage" here means reaching the age of legal responsibility. As for the second verse (And those of your women who have passed the age of menstruation, if you have doubts, their waiting period is three months, and also those who have not menstruated), it clarifies the waiting period ('iddah) for a divorced woman who has not menstruated, whether due to old age or young age.