Actually that set addition has always bugged the hell out of me. If it was directly attached to the intermix chamber things would make more sense. But the location leaves its actual function, or at least its function in what we know about M/AM reactors, a bit of a mystery. And I would be a liar if I said I had not spent hours thinking about it. (I used to travel a lot in the car and spent time thinking about things like this to keep my brain occupied.) I came up with several ideas to explain what Spock was doing in a room that was beside
the reactor core. One of them mirrored Timo
My pet theory is that it's the same thing as the pair of cylinders on the engineering floor in TOS: a location for inserting the all-important dilithium crystals into some sort of a carefully shielded dumbwaiter/waldo system that takes them to the heavily armored reaction chamber in the bowels of the ship.
My second idea and favored explanation was that Spock was accessing a controlling subsystem, reactor power station or cooling manifold. By manually adjusting this obviously irradiated system he was able to bypass the main energizers and get the reactor back up and running.
As for the plexiglass walls, I just assumed they were some sort of insulated transparent aluminum. It could even be protected by a low level forcefield like the warp cores of the 24th Century are (even though I think that idea is completely silly).