Olive can be rooted from leafy cuttings, and that is the standard method of propagation, but they are substantially more difficult than figs. (Figs have got to be the easiest plant on earth to root, with the possible exception of willows).
Yes, they like hot growing conditions, but they also need quite a lot of winter chilling, which is why they grow here in Florida but almost never set a crop of fruit, whereas they do wonderfully well in a climate such as Davis California -- hot summers, but lots of chilling in winter, without any extreme cold.