I'm confused as to how initiation interval is determined. I understood that it will be the length of the longest cycle in the dataflow graph, but I am confused as to how this cycle is determined. What line / part of the code corresponds to this cycle? Is there an intuitive way of thinking about it?

Since iterations in inner controller always execute in pipelined manner, the throughput of the system is bounded by the pipeline task that takes the most time to complete (similar to other calculations we did for pipelined execution performance). The formula tells you how long it would take the inner controller to complete N iterations. In this case the last line of code takes the most cycles to complete.

What is the longest cycle, from what I can see here the cycle starts at after the value sum has been calculated and loops back to this point once the value of reg has been updated., but that isn't when the loop logic begins. (Which to my mind isn't where the cycle occurs).