Yes, it will.
The LANTAC Enhanced DI Side Charger BCG should be compatible with the R2000 rifle kit as it is designed to accept side charging AR15 5.56/.223 bolt carriers.
The LANTAC Enhanced DI Side Charger .223/5.56 Bolt Carrier Group will be compatible with 300 Blackout as long as you have a side charging upper receiver with a 300 Blackout barrel installed.
The LANTAC Enhanced DI Side Charger .223/5.56 Bolt Carrier Group uses a charging handle located on the RIGHT side of the BCG. It will be compatible with your Bear Creek side charging upper as long as your ejection port is located on the right side of the upper.
YOu have to use a side charger upper
Yes, it will.
The difference between the mil-spec bolt carrier and this carrier is the side charging-handle. This carrier will only work in uppers that are cut/machined for side charging-handles.
This BCG will fit those uppers but for function they would need to be cut for side charging.
Yes, this carrier can be run in a standard AR-15 setup. The full auto just means it has a M16 style cut and can be used in a fast firing application. Most AR-15 rifles use a M16 style carrier now.
Yes, this does have a 5.56 bolt of standard size.