One: psychologically, most people look at the index. When the index goes up, individual stocks go up.

Two: Fundamentally, the index is rising, indicating that it is not surprising that prices are rising and commodities are falling together.

Futures linkage almost.

Stocks are purely speculative things, and futures at least have the actual relationship between supply and demand of commodities.

Not all futures go up and down together, unless they are of the same type, such as thread and hot coil/iron ore. Soybean meal and rapeseed meal. Soybean oil and palm oil.

Not exactly.