Is the departure of pilgrims from Mecca to Mina on the seventh of Dhul-Hijjah without entering into a state of Ihram, and then entering into Ihram from Mina, considered a breach of the rituals of Hajj?

There is no harm in entering into a state of ihram on the Day of Tarwiyah from Mina, and the Hajj is valid, although it is better to enter into ihram from one's residence in Makkah. The people of knowledge have stipulated that entering into ihram for Hajj is sufficient for one who is in Makkah from any place within it, whether from homes or from the Haram. Similarly, there is no harm in not clipping one's nails or not performing ghusl before ihram, because these are Sunnah acts and not obligations.