Any of them get illustrations? And what illustrations does the Sigil chapter get beyond the one map?
None of the faces. Sigil only gets the map, one picture of a dragonborn where you can see the city above him and finally one of the entrance to The Great Foundry (I think). Kinda sad.
Starting with the 'loths: what is said about A'kin and Shemmy?
A'kin is a raavasta and owner of the Friendly Fiend, an exceptional magic trinket shop. He seems to know a lot of secrets.
Shemmy's range of knowledge is only matched by her vicious temper. She is the most prominent chant-broker in Sigil, a position gained via a huge network of spies. She ensures that the power players of Sigil rely on her. She controls several powerful characters by having ensured their debt, such as Autochon the Bellringer and Ramander the Wise. Due to all these things, she is the most hated, feared and powerful creatures in the Cage.
The potential 'loth-spawn: Kylie?
Kylie is a tiefling that worked for Autochon, but when she quit and he (it?) wanted to kill her, Shemmy stepped in and forbade her killing. She now runs her own gang of couriers.
Those working for the 'loths: Adamok Ebon, Autochon the Bellringer, Ramander?
Ramander: Master of Portals. He buys land with portals or extorts those that own it until he pays Ramander big fees.
Adamaok: Bladeling hunter and assassin, sometimes work for Shemmy.
Autochon: Master of Couriers. Controls most messages that are passed between the residents of the Cage. He uses magically enchanted couriers to ensure that only the one supposed to gets the message. He is also rumored to have a deal with the Temple of the Abyss.
All the above covers most mentioned, but paraphrased (to varying degree).
Any mention of former Faction bigs and what they're up to in the current political climate? And who sits on the Sigil Advisory Council?
Council has 9 seats, but only one is mentioned. Rhys, former leader of the Transcendent Order.
Other power players mentioned are the Sons of Mercy (led by Swan's son), the Mutual Trade Association, run by Shemmy, Estavan (oni mage) and Zadara (storm giant).