Chapter 2 should come as a relief to anyone troubled by Chapter 1. There is plenty of exposition and much of the murkiness of Chapter 1's brain-weave clears up as affected characters converse with one another. Chapter 2 is a direct continuation of Chapter 1.
All the events of Chapter 2 occur "later that night."
Here is the basic structure:
1) Freddy and Biddy
-At the Scatterbrain Lounge
-At Michael Fountain's Apartment
-After Fountain's Apartment
2) Freddy and Selim
-At the City Museum
Also, structurally, the most important thing to note is that this chapter is (almost) entirely a wall of dialogue. The plot is propelled through the conversations of the characters. It's a verbal feast and makes me yearn for a great radio play adaptation of the play produced by Jim Freund and Stefan Rudnicki. Then again, if the novel ever got adapted into a television show, I can see Episode 2 (adapting Chapter 2) accomplished in one virtuoso tracking shot, following "action" from bar to street to apartment to street to museum.
Conversation #1 - Freddy and Biddy at the bar transitioning to Freddy and Biddy on their way to Fountain's.
Conversation #2 - Freddy and Biddy speak with Michael Fountain.
Conversation #3 - Freddy and Biddy post-Fountain.
Conversation #4 - Freddy and Selim at the City Museum.
So, what do we learn from these conversations?
-Freddy "had the notion that perhaps Carmody Overlark... was the same man as Khar-ibn-Mod, a Mameluke diplomat who served an Egyptian Caliph some  years back."
-Carmody Overlark "..changed his name...From Charles to Carmody, and just about two years ago." He has a reputation, possibly "inserted back in time a little," as "an intellectual, a legend, an amateur of all the arts, and a patron." His face is "probably Moravian." He "suffers from asthma--these last two years."
-Michael Fountain's nephew was most definitely killed by the brain weave. Micheal Fountain himself slipped the brain weave "almost completely." He does not know who they did find and change, "But it was somebody whose mind has touched mine, who was in a certain accord with me, a young man's mind, and I do not know whose." [Attentive readers will remember the name Miguel Fuentes from last chapter though the relationship is still a mystery.]
-Goal of the Harvesters?
Fountain: "You will attempt mutation on yourselves, or perhaps it will be mutilation. It will not work."
Biddy: "It will work! We've seen the castle on top of the hill. We'll climb that hill, we'll be the first people ever to climb it. We'll be the first super-people, the first people able to grasp the vision. And we'll lead the rest of humanity up to it." .... "Despise us, loathe us! We'll show you. We'll redeem you all. We'll make the breakthrough to intellectualized, celestialized, chthonized, socialized, paranaturalized, cosmosized, one-other-word-that-I-forgot." (yes, Lafferty is having fun here!)
Freddy: "my own girl has turned into one of the snakes."
Finally, Freddy pretty much lays out every bit of the plot thus far to his friend Selim:
Selim: "Is it the live things or the dead things that are bothering you tonight, Freddy?"
Freddy: "It's those things that won't make up their mind which they are. See, there are these brain folks that Biddy runs around with, three Shes out of Haggard and three Borgia types out of Baron Corvo. They mix up this brain stuff and put it out in psychic jolts. It knocked me to my knees the first time they used it on me. Tonight they tried it on Michael Fountain. He slipped them, but it killed his nephew and bit into someone else. Now they're raising up something that would be better dead, and they've put me onto a man who ought to be dead."
And a little later, Freddy: "You get plugged into their brain-weave and you stay plugged in. They plug into someone else, and you're connected too. And sometimes now I'm connected with [Fuentes] when they're not."
(If you're still confused by the novel, read that a few times. It should clear everything up. Once you've read it a few times, have fun looking up Shes out of Haggard and Borgia types out of Baron Corvo.)
Finally, Freddy learns a little more at the museum. "The life-mask is that of a civil servant who served under Akhnaton, the heretic king of Egypt.... lived around 1350 B.C., or around 900 B.C., if you follow the timetable of Velikovsky." The name of the mask? - "Kir-ha-Mod.... transliterated as Kar-Ha-Mod."
Freddy: "It's the same face three times, it's the same name three times."
The chapter ends with Freddy finding an address in his pocket. Freddy resolves to go to the address while hearing some Mexican-Spanish talk ("cooking up something big") in his head.
Some few other things....
-Scatterbrain Lounge is a great name for a bar.
-Hugh Hamtree gets my favorite laugh out loud lines in the novel with his helpful suggestion that the guy might have gotten froze in a block of ice. I love the idea of a bartender listening to Freddy and Biddy's crazy conversation and attempting to make a helpful suggestion.
-With all of the dialogue, the few spots of non-dialogue commentary stick out all the more. For example, see this post's title.