Do you have a pic of the whole tree. If it's a few leaves I wouldn't worry about it. If it's the whole tree, then a larger pic of the full tree and the trunk/planting hole may be beneficial with the diagnosis. Thanks!

Possibly. If you are confident that is the problem, give it a shot (so to speak).

There could be too much clay in the soil and/or not good enough drainage. I don't know about you but we have had a very wet summer here, some of my plants have chlorosis and some xeric plants looks a bit sickly even with good drainage although my Desert Willow looks fine. I can't complain (well maybe I can a little & I usually do) since we've been desperate for rain to relieve the drought. This kind of summer rain is unheard of and the humidity is off the charts. Anyway, one way or another we all seem to be diagnosing its too much water. I just saw a show on TV where they were saying we absolutely depend on ants because they aerate the earth's soil and help keep it from being compacted. I'd never heard that before so maybe the ants are a good thing?

I'd cut the bare branches back. Some years you get some dieback like that on the branch tips, often when the first freeze arrives extra early and the trees haven't gone dormant yet. That happened to mine last year. If your trees have survived May's rainfall, I expect the clay must drain well enough. In their native setting, they often grow in dry washes and dry creeks that only have water flowing through them in the monsoon season, so we know they can handle wet soil for at least part of the year. I doubt they'd be happy in waterlogged soil year-round. My original desert willow was planted around 2003 or 2004 and is in the worst clay soil we have up near the house. It drains terribly slowly. Despite that, the tree has done well. The one I planted more recently is in a sandier soil that drains better. While the soils in area where they are natives leans more towards being limestone-based, sandy/gravelly or caliche clay types, they grow pretty well in sand, sandy loam, clay loam and even fairly dense clay. I guess the question is how much rainfall they can handle in dense clay and this might be the year we get an answer to that question. If it helps any, they are related to trumpet creeper, yellow bells and catalpas, so if you can grow any of those in your clay [I realize yellow bells (Tecoma stans) are only annuals here], it is likely that you can grow desert willow.