Why does he invite me to his house without setting a date? he says "why not come hang out one day" insinuating future plans without specifying when?

[ZumbiGeneral]

Have you tried asking him to specify?
The way energy works, just seems like a talking point unless he's busy in his day to day. But overall communication is key. Sometimes you haft to communicate that you need better communication to be understood and reciprocated.