Yes, Jesus did come back from the dead, and is clearly stated in the Bible. And zombies don't always go around eating brains. Zombies are dead that come back to life, and I would call someone who was clinically confirmed dead but live a zombie. Also a spirit is the non-physical part of a person, and I emphasize part.
As one of the comments stated, I have to prove Jesus ate flesh and had no rational thought. Jesus didn't eat flesh, I get it. But you do have to admit "Symbolically eating his flesh and drinking his blood" to accept him is very...very 'symbolically' cannibalistic. And the no rational thought,
based on or in accordance with reason or logic.
"I'm sure there's a perfectly rational explanation"
(This is the only non-math definition)
Zombies can have rational thought, if one wants to get in somewhere they break a door or window open. They don't have enough thought process to turn the knob, but a certain scenario does. Nanobots