I know you can weild fire with your hands, but what about crafting fire arrows?
Do houses (other structures) burn?

No environmental damage (burning down houses).

As far as fire arrows, enchanting the bow with a fire enchant will catch the creature/person/enemy on fire when you shoot them for burning damage plus the arrow/bow damage.

The firewall spell creates long-lasting fire effects on the ground, although one could argue the ground itself isn't technically on fire, it's just a spell effect glued to the terrain.

It's also possible to set things on fire with other spells but it's just a short-lived visual effect, the objects won't take damage.