A: Adjusting the cable is not done by adjusting the axle position. Cable adjustment is done via the barrel connector at the cable/indicator junction for fine-tuning and moving the cable fulcrum clamp for rough adjustment. Axle position in the dropout is to adjust drive chain tension.

B: Axles are very tough and the nuts are soft. This is a design feature. Nuts strip so the axle doesn't. Replace the nut(s) and all will be fine. Parts should be available at your better LBS or if not Harris has all the Sturmey-Archer stuff. They aren't very expensive.