Is it true that Leonardo trained hisself to sleep 15 minutes every 4 hours? And if so, did he get a full nights in addition to that or is that all he slept? And if so is that healthy? And if so, how do you train yourself to do that? And if so…ok that’s all.
I remember reading that somewhere too (although I can’t cite the reference off the top of my head). It apparently allowed him to work 24X7 which doesn’t sound too healthy but then again he lived to a ripe old age… he also taught himself to write backwards so that it could only be read in a mirror. Why would you want to teach yourself to do this?
Well, I just read a shitload of Bio’s on Edison, trying to find a cite, but can’t. I did a book report when I was in grade school, and a few things stuck in my head. One of them was that Edison also took cat naps, on the floor of his factory/ shop in Edison New Jersey. “Menlo Park”, as it was called, was where HE worked 24/7 when he was hot on the trail of some new idea. Apparently he’d do very nicely napping for short periods, then working for extended periods of time. Wish I could find a bio that mentioned that fact, but I can’t. 
Cartooniverse
This never got answered so I’m just bumping it due to the purge that’s coming up.
I found a few references to this supposed habit of Da Vinci’s using Google. Mostly just other message board posters but nothing conclusive. However, do a search on sleep deprivation and you’ll get an idea of how unhealthy this could be.
This page shows that even a 30 minute nap in each 24 hour period is effective. This site also says that you cannot train yourself to get by with less than you really need but I’m not completely convinced of that.
I’ve heard that meditation can be more efficient than sleep and it seems plausible. We know that there are different stages of sleep. Let’s say we can determine that sleep stage X is more efficient than sleep stage Y and we usually only stay in sleep stage X for 1 hour each night. If I teach myself to immediately go to sleep stage X, and can stay there for about an hour, then I might not need any more sleep for the day. I think this is the conjecture behind those people who claim that an hour of meditation is like a whole night’s sleep.
Sleep deprivation can cause hallucinations and eventually psychosis if the condition is not treated so I’m not sure I’m willing to try teaching myself to get by with less sleep. Besides, I like sleep. 
This doesn’t answer part 1 or 2 of the OP but I think partially answers 3 and 4. The rest is left up as an exercise for the reader. 