Looking for Answers about Nikon Inc. SB-910 AF Speedlight?

Typo alert from the Staff: Three! groups.
Three: A, B and C

Yes, you can have different output and you can control all the 3 groups off camera with the SC-28 and SC-29.

Sure, as long as the SB910 is in master mode and connected to the camera either on the hotshot or by the SC28 or SC29 it can handle 3 zones of flashes each one at different outputs. You can even mix iTTL with Manual flash on different channels.

Using an external AC power supply for the SB-910 is actually a great idea; it decreases the 'recycling' time for the flash to be ready to be used again; just keep in mind that even if you use an external AC power supply, batteries still must be inside the flash, so consider purchasing 'rechargeable batteries'; and in the SB-910 manual says: "Do not use Power Cord SC-16 when connecting the SB-910 to the Nikon DC Unit SD-7; use the SC-16A instead". There are also battery packs which can be used externally, but I believe your question is about using AC power.

The Sd-8A and SD-9 can be used with the 910 so you should be able to use an external power supply of some kind.

Yes, it is built in the top part of the flash's head, and there's also a 'built-in wide panel'; this feature allows you to use only one or both at the same time; depending on your light needs.

Also do not mismatch, use four of the same type of battery.

Yes it will work if mounted on the camera, however, if you are wanting to use the flash off camera then you will either have to use it in SU-4 mode or get something else like the SU-800 to control it as the D3200 has no built in commander to control flashes.

No, SU-4 is built in to the 910.

Or use the flash in SU-4 mode but that would mean you have to set the flash power manually.

Yes, use the D300's in built commander.