I'll organize these by page number -- I'll use the page numbers in parentheses in the margins.
(6) Who is Algy? I notice he's mentioned on p. (37) as well.
(6) Does hyperborean mean "athiest"? Why?
(8) "I'll bring down Seymour and we'll give him a ragging worse than they gave Clive Kempthorpe." Who are Seymour and Clive Kempthorpe? Seymour shows up again on (22).
(8) What the heck is omphalos? (Okay, Wiki says omphalos stones (a religious artifact) were said to allow direct communication with the gods. There was one at Delphi.)
(10) Why does Buck call Haines "the Sassenach"?
(12) Stephen remembers how he carried the boat of incense at Clongowes. Was he an altar boy? Or is that where his mother's funeral was held?
(14) An unusual euphemism for God, I guess: "the collector of prepuces." (A prepuce is a foreskin or clitoral hood; since the foreskin is removed at a briss, God must have a collection. Naturally, this is Buck's joke.
(16) and (17) Okay, "Agenbite of inwit" has me baffled. Is he a character Stephen and Buck are creating to tell Haines about? Wiki says its a poorly translated piece of prose that gives clues to what 14th century Kentish dialect was like.
(18) They call their tower an omphalos. Interesting.
(18) Buck calls Stephen "Japhet in search of a father." Japhet was one of Noah's sons. This is also in the Hamlet discussion. (And come to think of it, this chapter is informally called "Telemachus," and Telemachus was Odysseu's son, who was searching for news of his father.)
(20) I like the wordplay in "Joking Jesus": "What's bread in the bone cannot fail me to fly." Jesus's bones (his body) were, after all, also Bread. (As would Jack of the Beanstalk's, had the giant his way. But that's probably neither here nor there.)
(20) I like that Haines isn't quite sure how to react to Buck's mocking of religion. Mustn't upset the natives. I also like that Stephen says he hears "Joking Jesus" three times a day, after meals... making it sort of an anti-prayer.
(20) I'm a little lost about Stephen's ashplant. Not sure what's going on there. (I think it's mentioned before this page, come to think of it.)
(21) Haines calls German Jews Britain's "national problem." Considering there's a lot of antisemetism coming from a character in the next chapter as well, I'm guessing this will be a recurring motif.
(22) "Says he found a sweet young thing down there. Photo girl he calls her." "Snapshot, eh? Brief exposure." How I love innuendo. I get the impression (from something I read online, can't remember where) that this is Leopold Bloom's daughter. I've only gotten to Chapter 4, so I haven't met her yet, but from what I recall she works in photography somehow.
"Brief exposure." Heh.
(24) The seal is a usurper? WTF?
So those are some questions I had while reading (and rereading) Chapter 1. If you've got answers, toss 'em in the comments (or if they're long, make a post of their own. I'll do some looking into this myself, too, and post what I find.