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The ants are there likely due to another infestation; they are attracted to the honeydew residue of the pests.
This link will help you.
https://www.gardeningknowhow.com/edible/fruits/figs/keep-ants-off-fig-trees.htm

You should have a tree professional come out to take a look.

Your local extension service can help. This article will help you to find the closest one to you: https://www.gardeningknowhow.com/extension-search

This is going to be an interesting answer. So, figs have a fruit that CONTAINS the flower within! Usually, they are pollinated by certain wasps that will crawl into the fruit and lay its eggs. This action is what pollinates the fruit. The baby wasps crawl out as the mature wasp dies. The fruit, then, swells from a small black fruit to its mature size and color. Some of them don't get pollinated and fall off before they swell.

Some varieties don't require this, and are self fertile, so it will depend on the variety that you have. Still, it won't have room or nutrients for all of its fruits, so many can still drop before swelling, even if they are self fertile.

This article will give you more information on fig drop if it starts to become an issue to where it won't produce: https://www.gardeningknowhow.com/edible/fruits/figs/fig-drop.htm

Normally, although it is very dilute already, you will dilute the peroxide even more before you use it. The oxidization is too much for some plants, so it is best to test small amounts first.

I would say that it can be safe to replace 1/4 of the water in the mix with peroxide. I just wouldn't recommend doing that full strength. This is especially true since using neem oil already carries a risk of damage to some plants. This is exacerbated by intense light and heat. Adding too much of an oxidizer may intensify this as well.

If you do intend to experiment with this, make sure to dilute it out and replace only small amounts of water at a time.

There are many other ways to battle fungus, as well. This article will give you more ways: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

Typically, a fig tree will not fruit until it reaches two years old, but it can take some trees as long as six years to reach the right maturity. There is nothing you can do to speed up the rate a tree matures at. Good soil and water management, time and patience are the only fixes for this.

https://www.gardeningknowhow.com/edible/fruits/figs/how-to-grow-figs.htm

I have never tried "it" but I have always heard that you can take a branch of an apple tree, graft it to (say a pear tree) pear tree and the Apple Brach will always bar Apples while the rest of it bars Pears.
Check out Grafting one tree to another. I think your answer lies there.