How did Aradia stay around as a ghost after she died? Do all trolls become ghosts after dying and can linger around? Or was it because of the game? Or maybe because she's a rustblood and can commune with the dead?

There’s a difference to be noted here- The Dream Bubbles are not the normal Homestuck Afterlife, they are something Feferi told the Horrorterrors to make. The mechanics of what happens to dead people in Homestuck is, as such, largely unknown, although it may operate on the ‘usual’ rules- Unfinished business stays haunting the place, while peaceful deaths ‘move on’.

That being said? There’s also the possibility Aradia’s hidden Dream Self was unconsciously Communing with herself and keeping her Ghost summoned and active.