Question 1: During a creature's movement, he moves into more than one fire space. Does he take the damage for each square?
Question 2: Using Forced movement (push/pull/slide) does the creature take the damage for each square entered?
Currently update to wall of fire notes that:
Creatures can take damage from the wall only once per turn.
In the past, this was ruled differently, see the edit history of this answer for previous interpretations.
At least now it's a lot simpler. Now it doesn't matter how large the creature is nor how many squares it moves, it takes damage once per turn. Still, if multiple PCs are playing ping-pong with a mob, they will indeed take damage every PC's turn that they enter the wall.
"Effect: You conjure a wall that consists of contiguous squares filled with arcane fire. It can be up to 8 squares long and up to 4 squares high. The wall lasts until the end of your next turn. Any creature that starts its turn adjacent to the wall takes 1d6 + Intelligence modifier fire damage. If a creature moves into the wall’s space or starts its turn there, the creature takes 3d6 + Intelligence modifier fire damage. Entering a square occupied by the wall costs 3 extra squares of movement. The wall blocks line of sight."
I think the intent was for a creature to take damage once (though I can certainly see how it may be interpreted as take damage for each space, the phrase "the wall's space" doesn't explicitly say each space).
It does say that each space takes 3 extra squares of movement (4 squares total for each square -- painful to get out of/cross).