there is a curve to it, up to a certain temperature it helps and then it starts making things worse (because it becomes a convection oven).

I believe it's around 35 Celsius.

if you are outside you can attach water nozzles to the fan, the evaporation will cool down the air stream. doing it indoors has humidity implications.

Fans increase the efficiency at which your body's own cooling system (sweating) works by increasing the amount of air that flows by your skin, be it hot or cold.

Anything helps, when you don't have AC. Moving slightly colder air to where you sit, or moving away generated from your body, does make a ever so slight difference. Helps to get rid of some sweat too, if you're sitting and sweating, which also helps a tiny bit.

Lived in the California desert with no AC as a kid, fans definitely help. Especially if you are sweating or spritz yourself with some water

But a fan is nice in not-heatwave but still warm temperatures. I have a usb desk fan from a PC cooler manufacturer (Arctic I believe) and it's one of the best accessories.

A fan is better than nothing, even in a heatwave.