Kakashi is not part of a clan
He got his blade from his father. Sai has one that looks like it. I guess Sai's from the Hatake Clan too?
Although Sai has a similar looking blade , it does not use chakra and more importantly the chakra coming from the sword is white. The fact that Kakashi received the blade from Sakumo raises the question of 'Where did he get it from?' and also the question of 'Why is Kakashi's chakra white similarly to Sakumo?' These two questions can be easily answered if we assume that Kakashi was part of a clan , most likely the Hatake clan.
He's smart because he's smart. You can't pass down intelligence through DNA.
There have been many articles and studies done to test and attempt to find which gene is for intelligence (such as
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) and the conclusion many have reached from these studies is that the neuron connections required to think and learn can be improved by genes giving them a type of "intelligence" so to speak as they can think and learn better than most.
He's strong because he's a talented prodigy who trained to get where he is.
I will admit that Kakashi has trained an awful lot to get to where he is now, however your genes can vastly improve the way in which your physical grow works - for example myself, I am too lazy to do sports but thanks to the athletic build that I inherited from my mother I can run, jump etc. above average and when I do exercise I build muscle strength and stamina much faster than many of my friends.