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As long as there are no pests in the depression and it is not rotting, and the bark around it is healthy, you don't need to do anything. It should be fine.

Fig trees normally need 2-6 years to bear fruit. If it had figs on it when you bought it, I suspect the nursery rooted a fruited cutting to increase the sales or maybe they had a fluke cutting that was able to bear the first year but still needs to mature before it could fruit more.

You may also have bought a truly mature fig, and if you feel this is the case, this article will help you to get it to fruit:
https://www.gardeningknowhow.com/edible/fruits/figs/fig-tree-is-producing-fruit.htm

If they have dried out or are mushy, go ahead and remove them. If they are still green and firm, you can leave them on to ripen.

You can unwrap it once temps generally are above 40 degrees F. If you get a few frosts after that, it will not harm the plant.

Some figs can survive in your zone. It depends on the variety. I would still wrap it if I were you, as a precaution. The figs that can survive in your area will survive a normal winter, but cannot survive a severe winter without help. Since you cannot know ahead of time which winters will be severe, it is better to be safe rather than sorry.

It sounds like you have a fungus, but it could be one of several. Treating the plant with a fungicide should take care of any fungus that are attacking the plant.

I would not prune it after leaves have appeared. It makes it more susceptible to disease if it is pruned after it comes out of dormancy.