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Depending on the type of metal that you used, you could be poisoning your trees. I don't recommend this for a tree that will get large. I recommend other methods for control.

This article will give you more information: https://www.gardeningknowhow.com/plant-problems/pests/animals/eliminate-gophers.htm

These articles will give you a few more options on getting blooms!

https://www.gardeningknowhow.com/ornamental/trees/jacaranda/potted-jacaranda-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/jacaranda/jacaranda-tree-not-blooming.htm

No, these methods are very outdated, and not proven to get results, since nails are not made of the same materials that they were when this was an acceptable method. Depending on the material that the nail is made of, it can cause the very quick death of the tree.

Beating it with a bat will either cause disease from the tree having to repair so many spots, or cause it to halt growth due to stress.

Jacaranda trees are notorious for this behavior and Those actions will, further, prolong flowering, unfortunately.

This article will help you to get this tree flowering again: https://www.gardeningknowhow.com/ornamental/trees/jacaranda/jacaranda-tree-not-blooming.htm

The tree is only evergreen in the warmest climates. Hardy in zones 9-11, the jacaranda tree will drop most of its leaves in cooler areas or during dry spells.
Your tree is too small yet to prune I would say, but here are instructions. The pruning article says to select a central leader and cut out competing branches. The spread comes from major horizontal branching in the middle of the tree.

https://www.gardeningknowhow.com/ornamental/trees/jacaranda/jacaranda-tree-information.htm
https://www.gardeningknowhow.com/ornamental/trees/jacaranda/pruning-a-jacaranda-tree.htm
https://www.gardeningknowhow.com/ornamental/trees/jacaranda/jacaranda-tree-problems.htm

This is a pretty devastating chop job for this tree. It may recover, but I would start worrying if after two years you don't see much recovery. That's about how long it will take this tree to recover from the damage done here.

Just keep caring for it as usual. (It doesn't really need much care, anyway.) This article will help: https://www.gardeningknowhow.com/ornamental/trees/jacaranda/jacaranda-tree-information.htm

You may try to brace the tree, but once it matures from improper pruning it will take an unsafe form.

The problem with topping, forcing branching, or trying to control a tree that is too close to a structure is that is usually leaves the tree unstable, or unbalanced. Ultimately, the answer may be the complete removal of the tree and starting a new one in another spot.

This article will help you to know what care these trees require: https://www.gardeningknowhow.com/ornamental/trees/jacaranda/jacaranda-tree-information.htm