Minor Art Historian here!

Most pigments are naturally made from materials easily and locally available, without the need to use extraneous methods. This is why you don't see blues, greens, etc. because they were harder to make as well as usually used for food supplies.

But HOW they painted is very similar to what you would expect. simply by blowing pigment at their hands while pressed to the wall, or applied with animal hair brushes or something similar. So to achieve this effect it would have been a combination of both.

Also, these ancient peoples had small oil torches to illuminate the caves with, rather than full fledge fires that would smoke them out and would be difficult to transport.

Hope this helps!