Spreading rumors about Garaam and just making it difficult for him to pass his final exam. Also information about Garaam participating in the Orpheus despite being first year was because of him. He was trying to make an image that Garaam skills are not genuine and he was just getting preferential treatment.
Simply because Youngjo is a play-boy, and also because he was the rumored person that Heejae brought in with his money. And yes, he did collaborate with Naeum to sabotage Garaam. I would say they were in a relationship up until chapter 63 where he got exposed by Heejaje. ( You can go read 63 again and all your question should be answered. )
When he was in highschool youngjo was in a "close relationship" (idk if they were dating or not) with the conductor of a church which was closely connected to the academy. Their relationship was found out and the conductor was labeled a pdf, but the real reason why he was fired was because heejae asked the academy director for it (heejae found out that the conductor berated yerim during a rehearsal). But youngjo didnt know that and felt guilty, so he wanted to ask naeun, the director's niece, for help. As an exchange, he planned to distract garam from his piano so that naeun could come on top among the first years.

Was youngjo from college just a flink or is he coming back?