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It should not be doing this. There are several things that could be causing this, from pests to fungus to too little water. Given that this has been a dry year for most areas and this is a relatively new planting, my first suspicion would be that this is a water issue. While these are very hardy plants, all plants need water to help them get established because their root system is not developed enough to find water for itself. I would recommend giving the plant supplemental water for a few weeks and that should correct the issue.

The soil may have an abundance of nitrogen, which would result in nice, healthy green growth but little to no blooms. Without the right amount of phosphorus, it will not bloom well. Bone meal is a great way to add phosphorus.

No, you should not eat these. All parts of this plant are considered toxic if ingested, and some people (those sensitive to it) may even suffer from contact dermititis (rash) by handling these plants.

A fungus may be affecting the leaves. Many fungus can cause the leaves to die back but will not kill the stems. You can treat it with a fungicide, but at this late stage, you are unlikely to see the leaves grow back before winter.

Because this is a trumpet vine, yes you can do this. You may see that it is not as full the first year following, but it will fill back in in about a year or so.

I would guess that the nitrogen to phosphorus ratio is off. The soil may have an abundance of nitrogen, which would result in nice, healthy green growth but little to no blooms. Without the right amount of phosphorus, it will not bloom well. Bone meal is a great way to add phosphorus. You may also be able to speed up flowering by pruning back the leaders to encourage more side shoots, where the flowers appear.