A: The vine you are referring to is called creeping fig, Ficus pumila. The leaves of this plant are generally very small when it is young and then the leaves become longer and larger with age. It prefers shade to partial shade but it seems to handle anything except full afternoon sun. Creeping fig is highly drought tolerant but it does not perform well directly along the ocean where it might be exposed to constant salt air.
I just experience the fruit drop at a location on the island and was astounded at the high fruit production from these vines. I have been told by the owner, this has been the highest amount of fruit he has ever seen but his plants have been around longer then he can remember.
Creeping fig does not appear to be too picky about the soil conditions. It has been known to damage the outer stucco veneer of walls or buildings which may require repairs after a few years. Clipping the vines will keep them from getting out of control. By the way, the fruit is ornamental only – it is not edible. The publication attached is from the University of Florida – Dr. Ed Gilman. Photo is from the University of Hawaii. http://hort.ufl.edu/database/documents/pdf/shrub_fact_sheets/ficpuma.pdf