Yes, this BCG is compatible with full-auto and multi-function trigger groups and has been tested extensively with full-auto trigger groups.
Yes, this is a complete BCG and it includes the firing pin.
Yes, the Faxon Firearms 5.56/300BLK Gunner Light Weight Bolt Carrier Group has been MPI inspected and high-pressure tested to ensure the material is sound and without defects.
No, this BCG has a standard gas key installed.
Yes, this BCG will require some re-tuning and timing of the rifle. This can be achieved with a stronger spring and heavier buffer or with an adjustable gas block. The BCG is compatible with most action springs, including the Geissele Super 42, however, the exact timing your rifle requires will depend heavily on other factors so we cannot make recommendations for a specific build.
No, this bolt carrier is not compatible with short-stroke piston systems or conversions.
Yes you can.
You will very likely require a different spring or weight. You will need to verify what exactly is going to run best in your overall set up because there will be a bunch of variables that will affect what will work best. The caliber, gas block, buffer style and barrel will all affect the weight/spring recommendation. I would highly recommend sticking to standard parts including the bolt carrier if you want to guarantee proper function with a majority of the parts available for AR's, but if you plan on using a light weight carrier, you will need to mess around with your set up to find the ideal combination of parts.
I believe you can if under-gassed. I use a SA adjustable gas block, a cheap buffer with weights removed, and a Tubb's lightweight flat wire spring with my low mass BCG in my 8.4 300blk build. You may be over-gassed w/o the adjustable gas block.