sometimes it looks like the definite article goes before the noun. Can they be interchanged (before or after a noun), or is there a rule? It looks like the same applies for adjectives.

1. The Haitian Creole definite articles always come after the noun.
Example:
liv la → the book
machin nan → the car
tant lan → the tent
soulye a → the shoe
soutyen an → the bra
The examples above contain the 5 different definite articles you will see in Haitian Creole.

2. Sometimes Haitian Creole speakers use the French definite articles (le, la) along with the root word, and makes it one "compound word". Remember that you will also see the word without the French article (ex: sante → health) and you'll see the word without the French article (ex: lasante → health). Keep in mind that you may still use the Haitian Creole definite articles (a, an, la, lan, or nan) after these types of words.
Example:
larivyè a sèch. → the river is dry
or
rivyè a sèch → the river is dry

Yo te klouwe sou kwa a. → They nailed to the cross
or
Yo te klouwe l sou lakwa a. → They nailed him  to the cross.

other such words you may find in Creole are:
lemonn or monn → world
laverite or verite → truth
lalibète or libète → freedom
latè or tè → earth, soil
lagerizon or gerizon → healing
lapolis or polis →police
lavant or vant → sale
lagè or gè → war
lasosyete or sosyete → public, society

etc...
3. As far as the adjectives are concerned, there's a small groups of adjectives which come before the noun in Haitian Creole. See this link for adjectives.

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