There are are variety of different cooking methods we know of from prehistory. Spitted meat seems broadly common, in British Isles and Scandinavia there's evidence of heated stones and water pits being used to cook as well as spitted meat (Keating 1908:326), in Polynesia and other places there's evidence of essentially ovens - pits in the ground filled with hot stones and insulated with organic matter (Firth 1957: 94), clay baking and clay ovens were also used in various places in Europe.

Most of those methods would have naturally produced oil when cooking meat, which would have also helped the meat cook, through the animal fats liquefying during the cooking process. Meat was a higher percentage of the diet than it is now, and any animal fats produced would also have been consumed as they are high in calories relatively.

As far as an exact date there isn't one. It happened so long ago that there are no records of the precise occasion.

More of an ask archaeologists question. Fats were used as cooking well before written history.

/r/AskAnthropology would be where you want to go.