Prior to the W&H brain boost, I seriously doubt that Gunn had very much of a formal education, though Wes, Cordy, and certainly Fred would have been doing their best to remedy that situation, with direct tutoring and possibly self help courses from the library and the internet. As has been pointed out, he would have to become "street smart" at a very young age just in order to survive, protect his sister, and run a crew of vampire hunters. He's obviously a quite capable street fighter, though I don't see very much in the way of classical martial arts or boxing in his fighting style, and the same would go for his choice in weapons. The axe, while tremendously effective against an opponent who is vulnerable only to a wooden stake through the heart or decapitation, is, unlike a sword, not a weapon requiring much beyond strength, speed, and coordination to use effectively. Any sword capable of decapitation, i e a Japanese katana, a Chinese dao, or a European broadsword, saber, or cutlass, would require at least rudimentary training to use properly.
Basically, Charles Gunn could be described as a true survivalist, as opposed to those individuals whose definition of that term consists of stockpiling food, weapons, and ammunition in anticipation of the day when society goes down the toilet. Gunn is a person who actively survives, despite overwhelming odds, from day to day, now.
