Question

1. He built a fire in/on the mountain.
2. He made a fire in/on the mountain.
3. He started a fire in/on the mountain.
4. He lighted a fire in/on the mountain.
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Can we use all the verbs? Are they the same? What about the prepositions? Can we use both prepositions?

5. He set a house on fire.
6. He set a house on a fire.
7. He set fire to a house.
8. He set a fire to a house.
(Do we have to put 'a' before 'fire'? Which ones are correct?)

Answer 1

In the first one, all the verbs can be used, and are used. One does not build a fire IN a mountain, unless it's inside a tunnel. If it's above ground, it's ON the mountain.

No, "a" is misused in 6 and 8. You may set a house afire. "Afire" means the same as "on fire". You may set a fire near the house, on the roof of the house, etc., but you set fire to a house, you set a house on fire, or afire.