im so confused this story has love triangle or not?

Yes and no(? Technically professor is never meant to be taken as a possible Lead but he is there as a sorta third wheel to make things complicated between the couple

is professor the brown haired guy? does he ever have sex with the bottom/top?

Yes that's him, he doesn't have sex with either

ah damn I've been avoiding this manhwa for the longest time since it looks like it has love triangle. i can read it now since it's not (づ￣ ³￣)づ does the professor like, extremely annoying or he's just there as background character

Mmm well the story is in a very tense place rn, I would recommend you give a while to read it ╥﹏╥

don't wanna spoil too much but both ML and professor are messed up

There are visuals of the prof having sex with the MC. Not real, and it doesn't go on for long, but just be aware.