It's a very, very old movie cliché in the west, often used to signify "the characters had sex" in the days when such things couldn't be stated blatantly. The smoking was supposed to indicate satisfaction and coming down from a high. Since then the "smoking after sex" shorthand has continued long after you could get away with showing basically softcore intercourse in mainstream films.
^ Subtext at most, the movie focuses on the acceptance that people can't always stay together and they need to move on.
It's Hibike! tho, so you know their relationship is very much up to interpretation.
@Shadowofdimentio & @watermane2000: The small question mark between them is implied to be from Momo, i.e. she not only wasn't thinking of that, but she doesn't understand what Kyouka is talking about.
Ι think Nishikinos. I believe it's canon somewhere that Nishikino is her mother's maiden name and the husband took that name for the sake of the hospital brand. It won't hurt Nico/Nico-ni's brand at all, since Yazawa isn't even part of it.