This is gonna be complicated to explain, but I'll try the best I can to make it a lot of sense. When starting the boss of Robot Storm/Carnival, can you reset during a run/before the run starts as when the level loads, the times is wasted to about 5 seconds. However, pressing the reset button will deduct. So if this makes any sense to you, is this allowed? (If so, would it be Checkpoint Segmenting or not?)

I know what you mean, every boss has this problem where it adds some extra seconds when you first select it in the challenge menu. You are definitely allowed to do it from a restart (doing the stage in story mode also doesn't add the extra seconds) and no it's not checkpoint segmenting.