The bolt will not obviously but, the carrier will work if you swap the bolt out with a 7.62x39 bolt.
This Fostech AR-15 Complete Bolt Carrier Group is not compatible with 6.5 Grendel unless you change the bolt for a 6.5 Grendel model. While 6.5 Grendel and 5.56/.223 share the same carrier, the bolt is different. I would recommend the Cryptic 6.5mm Grendel II Bolt Assembly, which can be found by using the link below:
https://www.opticsplanet.com/cryptic-6-5mm-grendel-ii-bolt-assembly-complete.html
It does not appear to be polished but will be much easier to clean than a standard bcg.
The FosTecH Complete Bolt Carrier Group (Nickel Boron) weighs 11.6oz
Yes this bcg works with .300 AAC Blackout.
Yes, this is a standard full-auto M16 cut Nickel Boron Bolt Carrier Group.
Yes, this will work with: 300 BLK, 5.56, 6.5 Grendal
No, this bolt is designed to operate with .223 / .556 / 300BLK
Yes it will work for all 3 calibers.
Yes, it will work.