Certified GKH Gardening Expert
What you are seeing on the tree is lichen. It is not the cause of the problem, but rather a symptom. They tend to attach to shrubs/trees that are sickly and unhealthy. This article will give you more information: https://www.gardeningknowhow.com/ornamental/fungus-lichen/treatment-tree-lichen.htm
In regards to what may be wrong with the fig, I would take a look at the roots. You may have some root rot or the tree may have a fungus attacking it, so you should go ahead and treat it with a fungicide, which will actually get rid of the lichen too.