Fast growing trees and hedges for zone 7a?

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6. Depends on a lot more than zone 7a

That only covers winter hardiness. You also need to account for heat zones for summer stress and consider rainfall and moisture. 7a covers a lot of different environments.

In general, I strongly prefer plants native to the region as they will likely survive the various local stresses and will be most beneficial to the native wildlife. In places like NC, the critical issue for many plants is surviving the "drought" summers that have high temperatures and almost no rainfall from July until October. These happen about every five years and are brutal. (Unlike this year with almost daily rain.)

I don't have any shade tree suggestions without knowing a lot more about your weather and your soils. On the hedge, I strongly oppose bamboo in all circumstances.

For a fast growing natural hedge, I like wax myrtle. It is great for birds and hiding a pesky neighbor or an eyesore. If there is enough room to support the height, I sometimes mix the wax myrtle with red cedar. That provides some variety in the appearance and in the wildlife that is attracted.