Near the end of episode 1, Brother Day (Lee Pace) briefly appears shirtless, revealing he has no belly button. Being a clone, he would not have been born with an umbilical cord.
In the books Seldon never goes to Terminus. In fact it is a critical plot point that no-one with any understanding of psychohistory goes there.
The library that Seldon, Raych, and Gaal meet in on Trantor is Trinity Library in Dublin.
This episode basically adapts the first part of the first Foundation book, simply called "Foundation" and published in 1951. The part in question is called "The Psychohistorians", and was written and published after the other novellas which comprise the Foundation trilogy (published as short stories between 1942 and 1950). It is by far the most faithful episode to Asimov's series, as the basic plot is kept, with many of the same story beats and characters (this is not the case at all for the rest of the series).
Amongst the changes:
And yes, compared to what follows, this is fairly faithful.
- the genetic dynasty doesn't exist in the books and has been completely made up, so that they can follow the downfall of the Empire in parallel to the story of the Foundation while keeping Lee Pace's face on the posters;
- the gender-swapping of several major characters: Eto Demerzel, Gaal Dornick and Salvor Hardin (to be fair, there are almost no women in the Foundation series until Bayta Darell shows up in the latter half of the second book);
- Asimov didn't intend any of the characters to be anything other than white, as the only reference to skin color in the Galaxy happened in the prequel books (written in the late 80s, compared to the 40s for the original trilogy) so the diversity in the cast is quite welcome;
- Synnax, the home world of Gaal Dornick is simply described as a provincial world, it's not an ocean world inhabited by very science-averse folk;
- the episode adds the conflict between two far away worlds, Anacreon and Thespis, and its very real consequences to Trantor. In the books, Thespis doesn't exist, and around the Foundation are the Four Kingdoms, Anacreon being one of them; the enmity between these kingdoms doesn't impact Trantor like here, even though it becomes quite important to the Foundation very quickly;
- the vault on Terminus doesn't look anything like that in the books, it's just a vault in a building in the heart of the city, there is no "null field" with someone immune to it, and nobody cares about the vault until the 50th anniversary of the Foundation;
- the time jump between the events of "The Psychohistorians" and "The Encyclopedists" is 50 years, not 35 (this change was made to accommodate the plot twists at the end of the first season);
- the existence of the Prime Radiant is super secret in the books, and there is only one (it appears in the third book); here it's shown for everyone to see as if it's no big deal;
- there are alien animals in the series; in the books, all animals are slight variations of Earth's creatures, because everything came from Earth (which is a key plot point of the fifth book, "Foundation and Earth");
- finally, it takes two characters from the two prequel books (the last ones written by Asimov) and incorporates them into the story: Raych, Seldon's adopted son who is black here and missing his Dalite mustache (he's already dead by this time in the books), and Demerzel, who is the Prime Minister to the Emperor Cleon I and who urges Seldon to spend the rest of his life to work on his psycho-history project (in the books, he's revealed as a robot at the end of the first prequel book and he disappears suddenly early in the second one, i.e. decades and decades before the events of the pilot here).
And yes, compared to what follows, this is fairly faithful.