In Yakuza terms, nee-san (sister) can be used to refer to a elder sister (doesn't need to be blood related) within the tribe. In the manga, he says "So you have a life to live too huh, I leave (our) sister to you" Which could mean he is leaving Nezumi to the care of Ao-Kun.
And finally we...
Honestly I think the same, it's just a confusing artistic choice. Artist probably wanted the audience to know from the get go that they were all women and didn't want the manga to look like a Yaoi manga.
This story started with good potential...but got sloppy really fast. She gets accused of gambling...then decides to just enter a gambling den and gambles. Straight up has no awareness of danger (trusts the other guy extremely quickly) etc. The characters in this story just aren't really...