While not "normal" by the true definition, it can be somewhat normal in the startup world. Healthy is a different story and being productive is another question. What you don't know on the flip side is his exact sleep habits which you could be missing altogether. There are some people that nap and work in spurts of time. I have horrible sleep habits sometimes and if I am stressed I can have insomnia at times. But as an example, I used to get up at 3am work until 5 or 6am, take an hour nap, go to the gym for an hour, and then off to work. I would stop working around 5pm come home eat, relax, do housework, whatever else and take a nap until about 10pm. Then get up work till midnight and back to sleep. I found I was much more relaxed and had a ton more energy sleeping in small cycles like that. I also found myself sleeping in cycles on weekends even more. I would work 3-4 hours, nap an hour or two, work 3-4 hours, nap again, and over and over. What works sleep wise for one person may not work for the next, so it is hard to answer your question precisely.
As a side story, the first startup I worked for back in the late 90s during the first bubble the CEO was older and well respected among Internet companies. He had just come off the CEO position at one of the biggest data center companies of the time and was well connected. One day not long after I started I had an idea for the company and randomly emailed him at like 10pm. He responded around 3 or 4am. I was working night shift in the data center and emailed him right back (part with a sense of surprise that he answered me and part with a sense of surprise that it was that early in the morning). Long story short, it ended up becoming an open line of communication between us that if I had a question or needed something I would just email him at 3am and usually have an answer within minutes.
As for the other part regarding the bragging, I would just take that in strides. That's just part immaturity and part probably trying to make co-workers feel guilty for only working 10 hours instead of 11 each day. I think it also comes from the accelerator mentality of grind, grind, grind to have a demo product in a short period of time.
Regardless I wouldn't worry about it too much unless you start seeing problems such as him demanding employees do the same (i.e. expecting you to respond to emails at 3am) or having short temper with employees. I wouldn't worry about the little errors either. It is a startup there are going to be missteps along the way. Most likely his sleep habits will change over time as the company gets it feet well planted.