Almost all the dialogue comes directly from the book, except for the beginning of Episode 3, where their relationship develops through the centuries. However, we don't know just what was talked about when Sir Terry and Neil were considering what they would put in a sequel if they wrote one. Some of that may have been involved.
I liked when Sheen got to use his natural deep-note voice during the drunk scene.
I thought that was the actress doing the voices in the Madame Tracy/Aziraphale scenes, with the possible exception of "Ron".
In the novel, Adam doesn't have red eyes**, but he does have a change in his eyes: "not devilment, because that was more or less there all the time, but a sort of blank greyness". Dog, however, does have glowing red eyes at times: "the usual glowing stare" at the cat, and not wanting to be "back with the ole glowin' eyes". As for the other kids, I think that was the director's choice. I thought they did rather well in the "sealed mouths" scene.
As for the existence of Pulsifer and Anathema in the novel, consider: the basic idea was William the Antichrist. The Antichrist was predicted in Revelation. Revelation was a book of prophecy, and since Terry apparently disliked the idea of prophecy, he made Agnes Nutter the only accurate prophet. To connect that directly to the angel plot, Aziraphale was made a collector of books of prophecy.
The prophecies have to be brought into the story somehow, so they come to a descendant. Instead of having them as clunky chapter headings for the chapters in which they happen (which I recall was done in some novels), they are written in disorder and obfuscation, like those attributed to Nostradamus. So we have Anathema who has memorized and studied them all her life, and still gets some of them wrong. Her being rich is implied in the book by the prophecy about the Apple no one can eat, that someone in the family interpreted correctly. (That also implies that someone was in America at the time because Jobs had real trouble finding investors at first. It would have been very tricky for an English family to have invested back then.)
Pulsifer is a kind of Rincewind clone - he wants desperately to be a computer wizard, but has negative talent for it. It's his superpower to break computers, and he's aware of it* - he asks whether he can be allowed to do the numbers on paper (so someone else can enter them into the computer). He can do all the number-crunching on paper, which I think must be harder without the programs that do half the work for you. He's also alert to patterns - he noticed the anomalous weather around Tadfield. He's also the voice of freedom, asking Anathema if she wants to be a Descendant all her life.
Actually, Anathema isn't controlled by the prophecies as much as some people on other sites seem to think. She is free to misinterpret them, to fail to act on them, to reject them. It's just that she has studied them and seems to be the one who is likely to do something important, since Agnes said she would be present at the time and place - not necessarily to save the world, but she would be there. (Though it seems that Agnes did know, we aren't told the prophecies nobody interpreted correctly that might have given Anathema some more precise help. "He is not what he says he is" could apply to most of the characters in the book.)
*I identify a bit with Pulsifer, because I don't think like a computer programmer. I have broken computers by following the instructions _precisely_, to the point that I was given a new one because they couldn't figure out what I had done. Eventually I learned a deep distrust of programmers, which has saved me several times. I have twice identified deliberately bad instructions in a program, instructions that could only have been written to cause trouble with malice aforethought.
ETA: ** Having reread the book, I find that when Adam is assigning various continents to the other members of Them, his eyes "glow with the fires of Creation" - so he does have glowing eyes once, but it's creation energy, not necessarily hellfire.
