It then goes to 5.2, Save/Cancel. I have none.
Yes you do. Read "He Calls It Thinking" again.
MY take on that is that I would play "He Calls It Thinking" on step 5.3. Essentially, I think they are saying I wouldn't get to respond since, as I bolded, each response is resolved completely.
"He Calls It Thinking" is a cancel Response. What part of "Cancel the effects of a Response" is making you think that it wouldn't be played in 5.II?
I think my take on it is that A Lannister Always Pays His Debts would essentially "resolve" putting one of my characters into morribund. As a response, I play He Calls It Thinking to cancel HIS out, thus bringing that character BACK from Morribund.
"Moribund" is a one-way trip. You cannot bring something BACK from moribund. Do you see the part before where I said:
"The only effects that in this game that can take place between the initiation and resolution of another effect are Responses that specifically use the words "save" or "cancel." Those are the only true interrupts in the game."
THAT'S what is going on in your scenario. You are trying to use a cancel effect, one of the only true interrupts in the game, to stop the resolution of ALPHD and prevent your character from ever going into moribund in the first place. Showing the place where these "save" and "cancel" responses take place are the entire point of "5.II" on the chart. Perhaps it will make more sense if I tell you 5.II should probably say "Save/cancel responses to this Response effect"? Your opportunity to save/cancel against the things that opened the window came back in Step 2.
Does this make sense?
Not really, because I am not sure how you are reading everything else so carefully, but failing to connect the fact that as a cancel, "He Calls It Thinking" is played in 5.II of the sequence started when your opponent played ALPHD in 5.I.
On the other question, you're being a bit to literal about the "arrow from III saying 'Follow steps I through IV, etc.'" question. All it is telling you is that you keep repeating or cycling through 5.I - 5.IV for each (non-save/cancel) Response to anything that happened in Steps 1-4, or earlier in Step 5. It is not your opportunity to Respond to his Responses. Your opportunity to Respond to his Responses is folded into the opportunity to Respond to anything that has happened in the window. That "Follow steps I through IV, etc." bit is telling you (for both passives and Responses) that there can be more than one per window, and that each one goes through the sub-steps separately.
I could write out a big, long example, but what it comes down to is that "He Calls It Thinking," as a cancel, would be initiated and resolved within the steps for resolving ALPHD. If it wasn't successful (because he interrupted HCIT with Paper Shield, for instance) and your character died anyway, you now, as part of your normal Step 5 response opportunities, have the additional Response opportunity of "after a character you control is killed." You can either play a Response to that, and come back to Responses to winning the challenge later, or you can continue to play responses to winning the challenge and come back to responses to the character being killed later. You can play Responses to anything that happens in the window - main action, passives, or Responses - in any order. The order in which the things happen have no impact. 'Follow steps I through IV, etc.' meant that this was your chance to Respond to his Responses, the order would matter and the rule about Responding in any order would not be true.
Mostly, it sounds like your confusion is that you are misunderstanding when cancels and how cancels, particularly cancels to Responses, are played. Remember the "except for saves and cancels" part of "resolved completely before another can be played - except for saves and cancels."