Purpose of cooking oil

I'm going to only answer the bit about oils in cooking, rather than all the uses of oil in the kitchen.

When frying or sautéing, oil acts in several capacities:

1. First, and most critically, the oil in a pan conducts heat from the hot pan to the food being cooked. The oil greatly increases the surface are of the food in contact with heat, rather than have just the bits directly in contact with the pan get hot.
2. The oil prevents (sort of) food from sticking to the pan or pot.
3. The oil (indeed any type of fat), is an important flavour carrier. It makes food taste better by bringing out the flavours.
4. Oil facilitates the Maillard reaction, which is how we get the lovely fried crust on the outer surface of fried foods.

Oil (olive in particular) has been in use for at least 8000 thousand years (according to wikipedia) around the Mediterranean (Greece, Palestine...)

So it has been used for a long time.

Before that and from other parts of the world, people used animal fat, either pork fat or goat fat (or whatever animals were around).

Butter has also been used for a long time, mostly in northern parts of the world, but it is not stable enough (spoils easily) for long term storage; milk was instead turned into cheese which is a lot more stable.

Each type of oil has its own significance, taste and flavor. There are dishes like those which are steamed which do not call for oil at all. But there are lot many dishes for which atleast minium quantity of oil is a must. Oil, does help in lots of things. First of all , it helps to cook the food being fried or sauteed in its typical way. Ofcourse you may cook the same food using boiling or steaming but if you use oil, the taste will definitely be different. Said that it is up to you to use oil in a particular dish or not. But for fried foods ofcourse oil is must without needing mention. Also oil adds a natural desirable glaze to the dish which nothing else can impart. The taste definitely varies with using oil in the dish for better. Oil also has minerals which are necessary and the needed fat to maintain a healthy body. I think before the usage of oil, people would have lived completely on meat, which has its own fat, which may have been rendered during the heating process. For other things they might have stuck to other cooking options like steaming and boiling.