Is there wood available?

But you can't bring wood with you because of pests in the wood

Typically they sell wood up front. If they arent there there is a self serve that I beleive it's on 250th for $5 for a bundle. Otherwise if you do the hike in camping you can gather a good bit of fallen wood.

You could always pick up wood in boone stores/gas stations ie. Walmart, Fareway n such.

Yes

Firewood is for sale at the entrance to the park.