There is a fig tree in the Sacristry of our church. I noticed that some of the leaves appear shiny and sticky. What is happening? Will using Trounce be of help?

The fig tree may have aphids, which would account for the sticky material on the leaves. Trounce is as good as anything out there. Be persistent, aphids will hatch out on a constant basis, so you would be smart to spray every four days or so until the problem is cleared up.