The FAQ said that only the front half of the figure take the effect of the terrain.

For exemple if a spider is in lava. She move one space. The front half exit the lava to arrive on an normal empty space. She will not take damage from lava even if is back half enter a lava space. This is ok.

But what happen in the case of the dragon? Is it the two front space or the four?

I'd assume just the front two squares, though you could figure in the "half" part if your group prefers.

When the dragon moves straight, the second row is completely entering the new terrain, so it takes effect. When the dragon moves diagonal, the terrain takes effect if the middle square on that side is entering the terrain. When it turns, the middle square that's moving counts for terrain. It's way too complicated and should just have been given a FAQ answer, but I think it would work.

That particular FAQ ruling is seriously broken for a variety of reasons. It's written in an extremely unclear fashion (neither "front" nor "half" has any clear meaning in this context), and the self-justifying explanation it contains doesn't make sense unless the writers had forgotten how several terrain effects worked before their ruling. Applied strictly, it also says that large figures fall into pits when their "front half" enters it, but climb out when moving so only their "back half" overlaps it, which means you can't even tell whether a large figure is currently inside a pit or not without knowing how it moved into its current position.

Honestly, the best thing to do is ignore it and use the original rules, which in the case of lava means that a large figure only takes damage when every space it occupies is a lava space.

But if you insist on trying to follow the FAQ, I'd argue that you should take that "front half" trainwreck to mean that large figures don't suffer effects for "entering" a square if they occupied that square both before and after the move. That unambiguously handles all figure sizes, diagonal movement, instantaneous multi-square movement (knockback, teleportation), etc. and seems to be consistent with both the offered examples and the stated intent.