Full disclosure: I discovered the gate trick because on one of my earliest playthroughs way back when I completely forgot about the box with the button and was desperately searching for a way through.
You know something interesting? The cooperation between Russia and Mexico isn't discussed in the game itself, but "Juan Lebedev" is still an obvious nod to their close ties.
I should also add that killing Lebedev yourself after killing Navarre does indeed make a difference compared to killing Navarre after she executes him, because the game keeps track of whether or not you kill Lebedev yourself regardless of Anna's fate.
Additional music is the theme from Airwolf, "Betrayal/Forgiveness" by Apocalyptica, and the Top Gun Anthem.