Now, the hypothesis is that fasting is one of the ways we can induce autophagy. The problem is, we have no way to measure autophagy in humans at the moment. That means we can't prove that fasting=autophagy=cancer stopper. It also means we don't know what an effective dose of fasting is (24 hours, 3 days, 5 days, etc.)
Regardless, it seems you are on the right track.
"The Karlseder lab studying the relationship of telomeres to cancer discovered that the cellular recycling process called autophagy—generally thought of as a survival mechanism—actually promotes the death of cells, thereby preventing cancer initiation."
[1] https://www.salk.edu/news-release/in-surprising-reversal-sci...
Does it increase focus overall? I have no idea.
Quite a few times, I've been so hungry that it interfered with my thinking. I had to eat something to get my focus back. Currently sub-10% body fat and a pretty seasoned dieter, so I think I have a fairly good feeling for what's real "hunger" and what's just "craving food".
In 2 weeks I'll switch to a weekly 36 hour fast, but I have no idea how I'm going to deal with the hunger pangs affecting concentration. Maybe, as you say, it is something you can train yourself out of.
If you want a softer landing, I recommend the 16+8 fasting for a week before diving into multi day fasting. You eat at the latest at 20 (8pm), and not until 12 (12am) the next day. It will take some adapting, but it's better than the headache inducing "withdrawals" you'll feel jumping headfirst into 36h fasting.