Extrude: this usually happens when your lines are not connected. From very far out it can look like they are connected, but if you zoom in closely, you’ll see that the points are not connected. If you connect the sketched lines properly, the extrude should work as intended.
What happens if you delete that little part circled in red? Does it delete that small part only or the entire shape?
Sketch: with some of the earlier version you could hide sketches, but it’s not possible in the current version (technical reasons).
Battery life: yes, it’s on the roadmap to increase it.