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These trees are hardy in Zones 5-8 and, since you are Zones 6-7, you should have no problem growing it in your area. This map will help pinpoint your exact zone, depending on where you're located in Rhode Island: https://www.gardeningknowhow.com/planting-zones/rhode-island-planting-zones.htm

So sorry your weeping tree sustained a winter injury. When a tree has broken branches, the best course of action is to get the wound as neat and clean as you can. I would prune the injured area, if you have wiggle room to do so, so it is a clean cut.

You asked about grafting. You could attempt it with that broken branch via a whip graft but grafts aren't always successful and I feel that you really do not have to pursue that path. Your weeping cherry in its present state is salvageable. It will grow branches from the existing branches and will eventually fill in so you do not notice the injury zone.

For more information on grafting trees, please visit the following link:
http://www.extension.umn.edu/garden/yard-garden/fruit/grafting-and-budding-fruit-trees/

Improper pruning can remove blossoms. Pruning should be following blooming.
Cold snaps or temperature drops after buds have formed will kill the buds.

Nitrogen is important but too much nitrogen will inhibit flowering.
Skip fertilizing unless a soil test shows a lack of it.

You can apply some Phosphorous to help promote flowering.

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/bone-meal-fertilizer.htm

Yoshino cherry trees are rated for USDA plant hardiness zones 5–8 so you should be fine.

I am not sure about that particular variety, but typically ornamental cherries will not pollinate fruit cherries. A fruit cherry (of any variety but the same species) is the most likely to pollinate your fruit trees.