Fire can be used to fell a tree.      Stone axes are probably faster for felling small trees. However, larger trees require far too much effort to fell with an axe.
How did stone-age woodworkers drill holes in wood? Think about it, they had no metal for drill bits.... Times up. They used fire to dig cavities into the wood, along with stone chisels.    You can get a fair bit of control over where the wood is burnt by controlling where you remove the ash, and by using a straw or your breath.
Okay, for smaller holes, a version of the bow drill was used with something like an arrowhead.