SPOILERS
Feed the Fire Walkthrough:

Stage 1: You will need to feed the grass until you level up.

Stage 2: The axe allows you to cut trees and furniture. You also get access to the slime island which has slimes and oil. You can should feed wood and slimes until you level up.

Stage 3: The pickaxe allows you to break rocks for coal. You also get access to the mine which has the bucket. You can bucket oil from the slime island and burn it. You can also refine the oil to fuel for huge fuel boost. You should focus on refining oil and, while its refining, mining coal. Only mining coal will not be enough.

Stage 4: The sword lets you kill the village guard. This gives you access to the village. You should burn these villagers at the start to give a fuel boost. Then you need to flip the lever in the village cave to open the gate to the gun. With the gun you can kill the spearman and raid the nuclear facility. You need to destroy the uranium container with any tool you have and burn the uranium. It should be enough to advance.

Stage 5: ???