Zombies

If Zombies are dead, why do they need to eat people?  They don't digest anything--they're dead!  So whatever they eat just stays in their stomachs, rotting.  After they ate enough, they would explode--end of Zombie. 

Also, if Zombies are dead, then if they killed a person, that person would become a Zombie, yes?  So their little bits and pieces would be moving around trying to 'eat' the Zombie who ate them.  Which would be the end of that Zombie, right?