Q. Weeping cherry has two splits on trunk.
Cherry trees are very susceptible to having their trunks split. Often they will grow over the splits and not have any serious consequences. Fertilize in spring only. If there is growth in the fall or winter, that is the reason they split. Having bare spots on the trunks is a major concern. If the trunk is bare all around the trunk, it cannot survive. It needs bark to perform its vascular fuctions.
There is nothing for you to do that will fix the problems. As long as it leafs out in spring, it is alive.