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If you are seeing flowering buds right now, then it is NOT a good idea to prune these now. If this is vegetative growth, then it will depend on the exact species.

This article will help: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm

Adding fertilizers with high phosphorus, and potassium levels will promote bloom growth. Here is an article that will help: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-not-blooming.htm

They prefer full sun in the morning, with some afternoon shade; however, many will grow and bloom in partial shade.

Pruning will depend, largely, on the cultivar of your shrub. This article will help you to know when to prune by type: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm

Probably Hydrangea. Although there are other spherical flowers that are called pompoms, chrysanthemum, viburnum, dahlia etc
Here's photos of Hyrangea arborescens 'Anabelle' variety.

https://www.google.com/search?q=hydrangea+flowers&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiq0o3iz9zdAhULOY8KHXaDA4kQ_AUIDigB&biw=1524&bih=746#imgrc=HgxYJK19Zx6NSM:

Frost tolerance or hardiness is a major factor. According to the USDA Plant Hardiness Zones, your zip code is in Zone 6b. You can review the following article and plant list for some possibilities. Hydrangeas are really nice and on the list for your zone.

A local garden center will carry plants that are suitable for your area.

https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-6/plants-for-zone-6.htm

This is, most certainly, a soil born infection. This can be due to heavy rains, and excessive moisture, along with the fact that hurricanes are notorious for bringing in new pathogens that plants in a specific area are not acustomed to.

I would recommend dolomitic lime and wettable sulfur. Applying these together will help kill off anything infecting the soil, as well as condition the soil back to a more suitable pH. It also contributes nutrients such as sulfur, calcium, magnesium, carbonates and improves soil quality.

This article will give you a good breakdown of hydrangea care: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/growing-hydrangeas-hydrangea-care-guide.htm