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Most fig trees need to be 2-4 years old before they can produce fruit. I would say that your Texas variety needs a few more years before it is mature enough. The one from your brother's home may have been older when you got it or it may have come from a cutting from more mature wood or it is simply a variety that has less time to full maturation.

For the one that it not producing, I would give it another year or so. Just in case, I would give it a bit of bone meal. Figs are very susceptible to too much nitrogen, which can produce lots of foliage and little fruit. Bone meal will provide phosphorus, which helps boost fruit production.

If the soil was very, very dry when you got the plants, the soil may be resisting taking up water. Fill your tub or a large bucket with water and place the plants in the water and let them sit for about an hour. This will force the over dry soil to once again take up water and should help with the leaves falling off.

Fig trees do fine being heavily pruned, so that is not a problem. Prune as you need to. It will likely encourage the plant to grow more like a shrub though, depending on how big it is already.

Pruning it in the spring after new growth appears will help reduce the amount of fruit it produces. You can also call local food banks. Some have programs where extra fruits and vegetables can be donated. Some food banks will even come and collect the fruit from the tree for you.

You should always wait for newly planted trees to establishe themselves before attempting to prune. Generally, this can take up to a year. During this time the tree is putting all of its energy into growing roots, which is imperative for healthy growth. If you try to prune before your fig is established, it will simply revert this energy to healing itself, rather than growing roots, making it more susceptible to pests and disease.