My theory* - apartment was offline so long because they were resolving relationship issues. I think Park had a down low relationship he was keeping from Caroline and she found out or he finally told her.
Caroline's fling with Frisky wasn't an issue, because she was open about it and didn't hide it. It brought them more money, after all.
Currently, I think Caroline is seeing someone outside the apartment, hopefully if she is, they will make an appearance eventually.
They are probably co-habitating because Park has no where to go or is just in the doghouse for long term until Caroline lets him out.
As usual, the apartment is considered Carolines, she is the one RLC wants, so if anyone leaves, it would be him.
The theory about Park being on the down low is just simply from behavior observation when they were in the old apartment.