The Ballistic Advantage 5.56 Complete Bolt Carrier Group will be compatible with the Aero Precision M4E1.
Yes, the Ballistic Advantage 5.56 Bolt Carrier Group will fit and function in AR15 platform rifles chambered in .223, .223 Wylde, 5.56, and 300 Blackout.
The Ballistic Advantage 5.56 Bolt Carrier Group is not compatible with side charging upper receivers.
The Ballistic Advantage 5.56 Bolt Carrier Group will work with an AR pistol. The Ballistic Advantage 5.56 Bolt Carrier Group will work if the AR pistol is chambered in 5.56/.223 or 300 Blackout with a Mil-Spec upper receiver.
When using a bolt and barrel from the same manufacture there is not often going to be any headspace issues, however it never hurts to check and confirm for yourself.
Yes, the firing pin will be included with both models.
The weight is .74 lb for the standard and .75 lb for the nickel boron model.
It depends on the model. The phosphate bolt is machined from 9310 nickel-chrome-molybdenum case-hardening steel. The NiB bolt is machined from Carpenter 158 chrome-nickel alloy steel. Both have a forged gas key that is coated inside and out with phosphate or EXO NiB respectively.