Answer: Several possible problems come to mind, although it is difficult to make specific suggestions long distance. Growing a container fig successfully can take some trial and error to find the best methods that work well for you and the growing conditions you can provide for it. Depending on how long it has been in the container, it may be as simple as repotting it and/or stopping using the salt-softened water.
The heat should not bother the plant, so that is not a concern. It should be in full sun all day while it is outside and growing.
I think the salt from the water softener is a definite concern. I would suggest you use rain water or distilled water to water it as a build up of salts can interfere with the roots' ability to take up water. Keep the soil evenly moist while it is actively growing, never sopping wet and never bone dry.
I would suggest fertilizing regularly with a general purpose slow release fertilizer such as 10-10-10 plus minors per the label instructions and possibly also a foliar feed but use these during the growing season only. I would not use epsom salts; if you feel the need to add trace elements beyond those in the fertilizer containing "minors", then I would suggest top dressing with a good quality compost from time to time or an occasional foliar feed with compost tea. You might also check the soil pH, it should be roughly neutral or slightly alkaline, most good quality soil-less mixes formulated for container plants should be fine in this regard. (Do not use a fertilizer for acid loving plants.)
In the fall, stop fertilizing and begin watering a bit less. In late fall you will need to bring it inside once it has stopped growing. Store it in a cool and dark location for the winter such as an unheated garage or basement so it rests (temperatures above freezing but less than about 40 to 45F) or bring it into a cool meaning only slightly heated to above freezing greenhouse; during that time water just enough that the soil does not dry out completely. Repot in early spring if the roots are crowded -- ultimately moving it to about a half barrel size pot, then root prune every other year or so to maintain it there. Prune it back in winter by about half its size to develop a sturdy and compact branching pattern. Take it back outside in the spring as the weather begins to settle so it can wake up naturally with the season, resume fertilizing and water more as it comes into active growth.
There are some pest and disease problems that can cause mottling or leaf discoloration and drop, but I would first try to make sure the cultural conditions are good before worrying about those.
I hope this helps.
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