Pt3
Index is allowed to stay in Academy City for the moment, but Necessarius recommends her to return to England. She wants to call Touma to see if everything is alright, but she has no idea how to use the 0-yen phone (lolwut >.>).
Touma came in with about 10 girls with him, and Index was too shocked to see him with so many girls she forgot to be angry at him.
The beast-girl was just for laughs, like in Chaos2Frozen's fic here:
http://www.fanfiction.net/s/6452999/1/
Ie, some random girl he met and then came home with him. Even Index commented on how that girl wasn't someone from Touma's usual incidents.
Pt4
Accel and Shiage is watching Touma's trouble with girls from the sidelines. Their comments below (and this is just the general gist, not a word-to-word translation):
Accel: "wth, Musujime? What's she doing here?"
Shiage: "Touma, my lord and master, please teach me the ways of building a harem!"
Pt5
Rikou sensed Shiage is going down the path of unfaithfulness.
Pt6
The girls who came with Touma are persuaded to leave (but a lot of Bardway's underlings were fried by Mikoto before she left, and she told Touma he owes her a explanation)
Index took time away from biting Touma and talked to Accel, recognising him as the one that was looking for LO.
Bardway, Accel, Shiage and Touma sat down on the kotetsu and started the explanation about magic (and their incoming enemies). Fremea sat on Shiage's lap.