-Why does the armored guy yell Robert? Who's robert?
Robert is his son. Here's the description for Robert's Firecrackers, which you buy to turn into the Shinobi Firecracker prosthetic tool:
Firecrackers from across southern seas. Can be fitted to the Shinobi Prosthetic to become a Prosthetic Tool.
Makes a deafening sound, frightening to animals. Sold by little Robert and his father to raise funds for their travels.
Their voyage brought them to Japan, where they would seek the "Undying" in an attempt to extend Robert's life.
It's pretty much the only hint I'm aware of as to what's up with Armored Warrior and Robert. He's probably at Senpou seeking the rejuvenating waters for his son. Or maybe he gave his son over the monks under the promise that they'd use the waters to heal him, but he just ended up an experiment and died, and Armored Warrior refuses to believe this or is in the dark about it and got kinda maddened by his situation. Hard to say.
EDIT: Apparently the Ninth Prayer Necklace also says this:
Robert's father came from afar across seas to the south, in search of the Undying. Repelling a thousand blades was a small price for the blessing of rejuvenation...
Which I guess is really just further reinforcement, not much additional information.
-Why does the sculptor turn into a demon?
There's a lot surrounding this, but based on various interactions with characters (when sharing sake and such) you learn that the Sculptor was, at some point, being consumed by hatred, bloodlust, etc. and Isshin cut off his arm to somehow prevent him from being totally consumed (presumably so he couldn't act on his urges, not totally sure). You can talk to the old lady in the building where you find Tengu after the Gyoubu fight and she talks about how the flames of hatred from all the warring going on all eventually go somewhere, and it seems like, for whatever reason, the Sculptor is sort of the conduit for all of that. So he's basically carving Buddhas trying to stall it, but eventually once the central forces invade he gets consumed by them and turns into the Demon of Hatred.
-Sekiro in the middle of the story brings up Emma's sword skill, but i don't remember her doing anything to show off her skills at that point
I don't know that it's ever made explicit, my assumption is that she has some sort of tell, like a sense of alertness, her stance, marks on her hands, or some combination thereof that Wolf can pick up on as a warrior himself.
-Why doesn't Genichiro use the rejuvenating waters for his immortal army instead of trying to use Kuro's dragon powers against his will?
No idea, really. Maybe it's dangerous or taboo to consume the rejuvenating waters (or sediment) and so he prefers to take it upon himself to save Ashina rather than force it on his men. Maybe he only trusts himself with the power.
-Why does the owl stab Sekiro, and where was Sekiro when the invasion of the hirata estate is happening?
Well, we do find out that Owl is after Kuro's blood as part of his sole ambition to basically take over Japan (or something), so it might make sense if Wolf was trying to protect Kuro or something.
Maybe Wolf was preoccupied for similar reasons as to why the usual soldiers of Hirata Estate were. There was some sort of battle and that's why Owl arranged the invasion that night, he knew they were at their weakest. We really don't know much about what was going on with Hirata Estate, or what even the true memory is, so it's kind of curious. It's something I'm hoping lore experts out there dig more into, or maybe we'll learn more in DLC!
