Because it's a French expression and in French adjectives come after their nouns.
yes
It is the day before Lent which is a movable date (as Easter). It is generally in February.
That depends... If you mean Mardi Gras as a party holiday and not a day of 'religious' significance, then you probably party hard, joining street fairs, Carnival celebrations, etc. New Orleans is...
Mardi Gras, also known as Fat Tuesday, is a day of celebration before the season of Lent begins the next day, Ash Wednesday.