Certified GKH Gardening Expert
This article will help with pruning your dogwood tree: https://www.gardeningknowhow.com/ornamental/trees/dogwood/trimming-dogwood-trees.htm
Most established trees do not require fertilizer. However, if you do choose to fertilize young dogwoods, use a small amount of slow-release fertilizer. Use a balanced fertilizer or a fertilizer that is high in phosphorous.