Is this a true Arduino board or fake (i.e. Arduino license violation)?
As far as I am aware, 'arduino' does not make a 'carduino' board so yes, because it clearly says "arduino nano v3" on it, it is violating the arduino license if they do not have permission from the official arduino team...
It is ok if the board is not being sold. If it is just being used by the person who made it then it can say whatever they want on it as long as it is not advertised to other people as being an official arduino board...
Apart from that the board looks cool. I would recommend that the 'arduino' name part is removed and then it will be fine

Mowcius