Which is correct & why ?
"Woody Harrelson makes me wish there was a zombie Apocalypse."
or
"Woody Harrelson makes me wish, there was a zombie Apocalypse."
Please explain in detail. Thank you.

"Woody Harrelson makes me wish there was a zombie Apocalypse."
No comma in your sentence.

As a complete sentence, this is:
"Woody Harrelson makes me wish that there was a zombie Apocalypse."

Note the conjunction 'that'.
There are only 7 conjunctions that are preceded by a comma, because these conjunctions join independent clauses:

and, but, or, nor, for, yet, so.

my daughter tells me that the new rules say that you don't need commas in a list of adjectives... is this correct?

Are you referring to "new rules" taught in English classes? I'm curious as to what they are.

Commas are not needed if one wants to use "and" repeatedly:

"The music was great, but we left because the venue was boomy and hot and humid and crowded and too dark."

Otherwise, I believe multiple commas are still correct written English:

"The music was great, but we left because the venue was boomy, hot, humid, crowded and too dark."