My current understanding is that 下りる means to go down, for example, 階段を下りる (Go down the stairs); while 降りる means to get off some form of transport, for example, 飛行機から降りる (Get off from the aeroplane).
Is this understanding correct so far?
However, which one is used to "go down a mountain", and possibly other uses for going down?
おりる
andくだる
.