Is it permissible for spouses to uncover above the knee or to wear only underwear permanently at home? Does this cause the angels to depart? Is it permissible to recite the Quran from memory in this state?

It is permissible for one spouse to uncover their 'awrah (private parts) before the other, based on the Prophet's (peace be upon him) saying: "Guard your 'awrah except from your wife."

However, it is commendable to cover oneself out of shyness before Allah and the Guardian Angels, based on his (peace be upon him) saying: "Allah is more deserving that one should be shy before Him than before people," and "Beware of nudity, for there are with you those who never leave you except when you go to the toilet and when a man has intercourse with his wife. So, be shy of them and honor them."

The described situation does not prevent the entry of angels. Khadijah's (may Allah be pleased with her) action with Jibreel (peace be upon him) is cited as evidence.

As for reciting the Qur'an in that state, there is no harm in it, as long as the reciter is not in a state of major ritual impurity (junub), or in a filthy place.