I'm confused about using "pa" for possession rather than negation. How do you say "the car is not mine" vs the "the car is mine" (Machin nan pa m')? It's confusing because "The car is not good" would be "Machin nan pa bon" right?

You are right.  This can be confusing.
And yes, you got the translation right on "The car is no good"


Whenever you see the word "pa" in Creole, there's always a great possibility that it might be a possessive pronoun, especially if it's followed by a pronoun (contracted or non contracted) like this: pa mwen or pa'm, pa ou or pa'w, pa nou or pa'n, etc...

You'll especially be alerted when you see the Haitian Creole  negative indicator  "pa" right next to a possessive pronoun pa'm, pa'w, or pa'l, etc... in a sentence, like this:  Se pa pa'm nan. That's not mine.
. 
Just remember that with all the contractions (pa'm, pa'w, pa'l, pa'n) if you stumble on the contracted "pa't", this last one is not a possessive pronoun, it'S the contraction of the negative indicator 'pa' and the past tense indicator 'te'.

Here are some examples:

Sa se pa'm nan. (contracted)
Sa se pa mwen an. (non contracted)
This is mine.


Kote pa'w la? (contracted)
Kote pa ou a? (non contracted)
Where's yours?


Pa'm nan pi gwo. (contracted)
Pa mwen an pi gwo. (non contracted)
Mine is bigger.


Have you heard the expression:
Jodi a se tou pa'w, demen se ka tou pa'm.
Today is your turn, tomorrow might be my turn.


also,
There's a popular slogan in Haiti that says: Pa'm pi bon. Mine is better
People use it especially when they talk about religion :)


Sa se pa pa'l la. (contracted)
Sa se pa pa li a. (non contracted)
That's not his / hers.


Sa se pa ti bebe pa'n nan. (contracted)
Sa se pa ti bebe pa nou an. (non contracted)
This is not our baby.


Sa se pa't pa'w la.  Poukisa ou te pran'l?
That wasn't yours.  Why did you take it?


The car is mine.
Machin nan se pa'm.


The car is not mine.
Machin nan pa pa'm.
or 
Machin nan pa pou mwen (to make it easier)

Here is some links to other posts, including an audio one, about possessive pronouns.
'PA' is not always NEGATIVE
POSSESSIVE PRONOUNS
Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words