The 2A Armament AR15 Regulated Bolt Carrier Group might work with the Law Tactical folding adapter. However, I recommend contacting the manufacturer to confirm.
The 2A Armament AR15 Regulated Bolt Carrier Group will work in your DDM4V7 Pistol. I agree, the combination of the 2A Armament AR15 Regulated Bolt Carrier Group and the Geissele H3 Buffer and Spring should smooth out that the DDM4V7. I would also consider just switching out your gas block to an adjustable gas block like the one at the link below.
https://www.opticsplanet.com/superlative-arms-adjustable-bleed-off-gas-block.html
The A Armament AR15 Regulated Bolt Carrier Group uses a 5.56 bolt so it will not work in a 6.8SPC. The Bolt at the link below will work for 6.8SPC.
https://www.opticsplanet.com/bolt-carrier-group.html?_iv_gridSize=120&_iv_parent-caliber=6-dot-8-spc
Yes. It will be compatible with 300 blackout.
Yes, this will work with the JP Silent Capture System.