So here's my thoughts:
The beginning there, is the destruction of that camp we see with all the kids sitting on the tank, perhaps this is the destruction of Diamond Dogs.
When you see Big Boss smear the soldier's ashes on his face, if you pause at the right moment you can see he's still wearing the MSF badge. Which makes me wonder if MSF is still around for awhile, in some of the later scenes you see the Diamond Dogs logo so I wonder if Diamond Dogs gets wiped out at some point, and thus he founds Outer Heaven(which you can see a logo for slightly before the TX-55/MG Zeke/REX Hyrbrid and Skullface scene which seems to obviously take place in some sort of underground nuclear facility...again probably in south africa since they hinted at that at the end of GZ in the timeline, and Outer Heaven was in Zanzibarland, South Africa) perhaps with the help of Skullface or who knows maybe he teams up with him to take down Zero.
As someone else said, that is obviously Kid Liquid which makes sense considering the timeline.
Quiet seems to be getting dunked by some dude into a vat of water, then later she's pounding dudes heads in left and right.. not much to read here.
Other than that I don't have much else, we see a bit more of Huey as well...it looks like Ocelot injects him with Sodium Pentothal or "truth serum", or at least that's what I'd imagine it is considering it looks like it's during the torture scene.