Index movements are typically based on the arithmetic average of the percentage price changes for the stocks in the index.

It increases the quantity of goods demanded, and will cause a movement along (not shift of the curve) the demand curve.

The geometric mean reflects a buy-and-hold strategy.

The IRR would stay the same because the return on each dollar invested remains the same.
The NPV would increase since the difference between total present value of the future cash flows and the initial outlay also doubles.