That's a savant level first read there, you should be proud. Most people aren't piecing that much together until much later on. Some of your theories are spot on, others are so close but you've missed by a hair. And they all have merit. And there's maybe only one there I could say for certain isn't the case but it's a very interesting take nonetheless!
Spoiler free...there's the r/genewolfe subreddit which often has people on their first read and people are pretty good with spoilers but beware
I believe there's a podcast called Alzabo Soup that discusses the books chapter by chapter
There's a chapter guide someone wrote that looked good but you don't sound like someone who needs a chapter guide tbh! Maybe that's similar to the podcasts? https://www.amazon.com/Gene-Wolfes-Book-New-Sun/dp/1947614096
It’s so gratifying that someone else enjoys it. If Ultan corrects you, just keep moving forward! Amazon assures me that you can buy the print version here: Gene Wolfe's The Book of the New Sun: A Chapter Guide https://www.amazon.com/dp/1947614096/ref=cm_sw_r_cp_api_i_NZcXDbWF7F1R4