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Fruit trees are very susceptible to frost cracks or bark splitting due to the fact that they have thin bark. These are caused by drastic temperature fluctuations, especially in the winter or by warm sun on the tree in the winter time. This then causes sap oozing. It can be reduced by providing some extra protection to the tree, especially the lower part of the tree. Normally, a paper wrap is used to give the trunk some extra winter protection.

It was a pretty cold winter for many parts of the country. It may not have survived the winter cold. This article will help you determine if it is still alive:
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm

You can do some light pruning anytime, but for the health of the tree, if you need to do heavier pruning, you should wait until its dormant.

Weeping cherries are typically grafted rather than propagated by root cuttings. This article will explain how to do that:
http://www.ces.ncsu.edu/depts/hort/hil/grafting.html

I personally like neem oil. It is often sold as fruit tree spray and is used on fruit trees for this very purpose. It will work just as well to keep bugs from an ornamental tree too.