Is your Hajj valid despite not having the intention for Hajj after the 'Umrah, and exiting the state of Ihram after throwing Jamrat Al-'Aqabah, sacrificing, and shortening the hair before the Tawaf Al-Ifadah, and not spending the night in Mina on the thirteenth night, and does the husband's failure to make the talbiyah affect the validity of his Hajj?

Your actions indicate your intention for Hajj and the performance of its rituals, even if you did not vocalize them, there is no harm. Appointing someone else to perform the rami (stoning) is not permissible except for one who is incapacitated. Leaving Mina on the night of the thirteenth is permissible for those who hasten and depart before sunset on the twelfth day. The farewell tawaf (circumambulation) must be the last ritual. If it was performed before the rami, it must be repeated if you are in Mecca or within the distance of qasr (shortening prayers); otherwise, each of you owes a sheep. The talbiyah (chanting) is a sunnah and not obligatory. Therefore, each of you owes a dam (a sheep to be slaughtered in the حرم and distributed to the poor) for performing the farewell tawaf early and for not performing the rami on the twelfth day without a valid excuse. Your Hajj is valid, Allah willing.