Is the zombie apocalypse possible? Why or why not?

Likely but it is more likely to happen so don't worry.

Probably not, because when you're dead, you lose your 'soul'. Like, if you cut out someones heart and put it in someone's body, then yeah, it could work, after a certain time. However, a zombie's body is completely dead, so all the nerves are dead and such. It's just scientifically impossible.