K&F Concept EN-EL14 Battery and Battery Charger for Nikon EN-EL14 EN-EL14a Battery Compatible with Nikon D3500 D5600 D3200 D3300 D3400 D5500 Coolpix P7800 P7700 P7200 P7100 P7000 (1050mAh*2)

SKU: KF28.0020

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I've pretty much only used these batteries when doing video work, and haven't gotten any hum. Hope this helps. 
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Yes, they are rechargeable and fully compatible with the D5100 charger. 
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These batteries are in accordance with the en-el15b standard, and there is no problem in using them in the camera. They can be used while charging in the Z5, Z6II, and Z7II. There is Nikon Z7camera, works great 
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No, it's just a micro USB cable in the package. You need to use your own USB plug to charge it. 
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If they are compatible with your Nikon camera, they will also be compatible with the charger that came with your camera. 
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On the Z6, it does charge internally. 
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It depends on many factors, how much your lens autofocuses, if you use flash to turn off the camera, etc... 
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No, EN-EL15 is not suitable! D3 uses EN-EL4... You need to check the battery type that the camera is compatible with. I highly recommend the K&F batteries and chargers, I use them in both my D500 and D7000 Nikon cameras...depending on the camera settings I can take over 700 shots with the battery. 
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Personally, I charge the battery ahead of time or when I arrive at my destination hotel. I then store the battery in my camera bag, separate from the charger. So far, I'm happy with these batteries.