1. In Japan, in order for a sword to be registered, it has to be made by a licensed swordsmith, and has to be made using traditional materials (tamahagane) and using traditional methods. "Katana" isn't a word used to describe authenticy. Its more of a term used to describe length and purpose. If the sword isn't made traditionally by a licensed swordsmith, it can't be registered, and is considered something less than a genuine nihonto, and more or less an item suitable for iaito practice, or as a prop in a drama. (Or, it could be considered an unregisterable weapon, and be confiscated).
2. If you are talking about the tsuka, there is no fixed size, but its more or less defined by the length and shape of the nakago and the moto-haba of the sword (roughly around 3cm, depending on the sword). The thickness (moto-kasane) will be about 0.7 cm, again with some variation.