OceanCube's Things

I am looking for a yaoi manga that has a teacher student relation ship but there is a time skip and they get married and live together and the younger man becomes a teacher but he has a students who is a delinquent like he was who comes over and plays video games a lot and doesnt understand why he is together with an old man

thanks! i hope someone knows what this one is called its bugging me

I am looking for a historical manga or it might have been a webtoon about girls trying out for marriage with the emperor.

One of the characters time traveled and had an ipod with two songs on it. One pretty singing, one weird chanting. The mean girl used the pretty singing one. The MC used the chanting one and the emperor liked it? He asked her to do it again but the ipod died.

think the mean girl had red hair
I think it was set in Korea