It isn't possible to keep the HUNGRY and HAPPY meters full all the time.
The way the Tamagotchi is programmed means that these will decrease every so often - otherwise you wouldn't need to look after your pet in the first place! If you keep feeding or playing with your tama when it is on 4 hearts it doesn't mean that it will not go down to three.
I think that you probably can't get nazotchi as a proper pet - it only appears when linking different versions of Tamagotchi through infra-red, because the different versions don't have the same pets / graphics. This means if you link with someone who has a Ver.1 and you have Ver.2 with a pet they can't get, their device can't show your pet because it doesn't have a picture of it in its memory. To fix this they made nazotchi who will always show up instead.
It defeats the point of him existing if he is a proper pet. If he was then it would be silly if he was showing up on people's screens. How would you tell the difference between whether it really is a nazotchi pet, or whether it is just because of having different versions (apart from knowing which pet your friend has, obviously)?