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So Ocelot loses part of his arm during MGS1. Now, as i said before, ocelot has first hand (no pun intended) experience with robo arms because he hangs out with his ultimate man crush, Big Boss, in MGSV. Also, if PW is anything to go by, robo arms have been a thing since the 70s in the MGS universe.
so, when liquid dies, he gets his arm grafted onto himself before the events of MGS2. During the end of the tanker sequence of MGS2, you see that liquid comes alive and takes over ocelot. This is actually happening and not part of the hypnosis stuff that happens later. As an aside, when Snake gets out of the tanker himself and Otacon drop off liquid's body (minus an arm of course) in the wreckage of the tanker so as to fool people into thinking snake died during that event.
Fast forward to MGS4 and Ocelot has had Liquid's arm removed but decides to keep the whole liquid-is-taking-over thing going. He had to have it removed because that whole thing where liquid would possess his body got kinda annoying, you know? Hence his having a robo arm at the end of MGS4.
Now, remember Liquid's body? Well apparently someone picked up whatever the fuck was left of it after soaking in the hudson river for who knows how long and losing an arm and being persevered by crazy people for a few years and used it and parts of solidus's body to reassemble BB. I'm guessing they took Solidus's vocal cords because BB sounds just like him and not like Solid snake. Also, Big Mama knew that Solidus was the body that was burned at the end of act 3 but decided to have a breakdown anyway because story. She didn't even birth him AFAIK so it's all her not willing to break kayfababy or whatever that's called.
so yeah