why Killua hasn't discovered Nen from home. Seeing as even his littlest brother Kalluto knew Nen, how come he didn't at age 12?

• Silva and Illumi probably wanted him to learn for himself. That's why he was allowed out of their house by his father. Perhaps all this time, he'd been neglectful and inattentive (as how kids are) when it comes to Nen. He probably ignored it and regarded it as some special power he couldn't have. The thing with Killua is a big part of him is smug at his abilities. It's only when Illumi put a needle to his brain that he concede in battles.
• The household thought it wise to refrain from making him learn (and in fact even fear it, as Illumi inflicted on him) in order to easily control him.
• He was expected to learn it from Celestial Tower, but he left at Floor 190. To elaborate more, Silva had his sons enter the tower. From reaching floor 200, they were expected to have learned Nen by themselves.
• He probably has been using a special kind of Nen, the eyes thing he used with his mother. That's why his mother was afraid of him and could be injured by him because she wasn't sure herself what her son was capable of (for all she knew, he could be hiding his Nen abilities).