Let me be the first to welcome you to USA Carry, procop. Welcome aboard!
Anyway, North Carolina is what's known as a "shall issue" state, meaning that if you meet all the requirements under the law, you will be issued a permit. Also, even though NC only issues permits to its own residents, it honors resident and nonresident permits from 30+ other states, so chances are if you have a permit from your home state, you'll be able to carry there as long as you're not a NC resident. Also, it is legal to open carry there without a permit, even in a vehicle.
Finally, as for class III and NFA weapons, check this map:
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