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It is hard to say. It may, but that is a lot of branches to be removed. Even if it does survive, it could be years before the branches would regrow to the point where they were before. You may want to consider replacing the tree.

Now would be a suitable time to move your tree. The only other good time for transplanting would be fall.

While it sounds like your tree may be in need of some pruning at the top to remove the older, unproductive growth, if you can wait, I would. Pruning after it has started blooming and leafing out makes it susceptible to disease. If you need to prune it now, it will most likely be ok, but just keep an eye on it and treat any problems that might happen quickly. This article should help: https://www.gardeningknowhow.com/ornamental/trees/weeping-cherry/pruning-weeping-cherry.htm

If the tree had a tip blight or thrips, it is possible that all the new growth was killed off. This would leave the old growth alone and the tree is still relatively healthy, its just that new branches would form. Did you see any small shriveled branches fall to the ground in the past? This is normally an indicator of thrips or tip blight.

A balanced fertilizer would be best for this tree.

Around the base, anything that likes the shade and is relatively shallow rooted would be best. Vinca or dwarf azaleas would work. Hostas, lily of the valley and Solomon's seal would also work.

It sounds like you have shot hole leaf. This article will help:
http://www.ipm.ucdavis.edu/PMG/GARDEN/FRUIT/DISEASE/shothole.html