Yeah, I think paper is vulnerable to fire, but an arrow probably not. Thinking about it in real world terms, a fire that could vaporize a arrow moving somewhere between 100-200 fps would have to be pretty freakin' hot. Of course, thinking of it in real world terms is only so useful because its magic, but heck, you got to start somewhere.
Stormwrack lists spells which can start fires, and it lists Wall of Fire as one that can't. (I find the fire starting table a bit hinky in Stormwrack, but that's a separate issue.) They say that Fireball can start fires, but Flame Strike can't. Lightning Bolt can, but Scorching Ray can't. I was really hoping that I'd find some sort of correlation between spells that don't affect objects not being able to start fires, but that was apparently just pie in the sky dreaming on my part.
Dealing damage to the arrows seems like a pretty good ruling, though I'd go with the half damage to objects and I'd probably half that again to reflect the fraction of a second the arrow spends in the flames. Looking at the SRD I don't see anything mentioning the wall as being see-through, so I'd rule it blocks line of sight. (If the opague nature of the wall is mentioned elsewhere, I might go back on that.)