Unsure if this has been found before. Apparently, you can jump off the border of the one-hit kill (frame perfect).
How did I come to this: I'm usually a little ahead of the cycle and I just kept trying to jump right before death for fun. Now wondering if this can be applied anywhere else.
Yeah, works the same way on spikes. I don't know of any way to use it in runs to save time though.
Yup, this has been found before. Some of the older TASes use it to save lag-frames throughout the run.
It's possible on anything that's a one-hit KO object, such as the boiling water in Stage 3 or the spikes in Stages 4-6. The only use for it to save time realistically is to keep up with cycles, such as if you're slightly behind the bubble cycle in the video you posted Kuningas, or if you're slightly behind a cycle in Stage 5.
For example, I'm fairly consistent with getting a spike jump in Stage 5 if I'm slightly behind TAS cycle. Probably about a 60% success rate. It's pretty easy to get the timing for, but my "setup" for it greatly limits its utility.