Zombie spawns are mainly tied to FPS yes. Higher framerates will result in more zombies being spawned usually.

EDIT: To clarify, FPS isn't the only factor that determines zombie spawns, but it sure does help.

From what I know, screen resolution can also have an impact (though in what way or to what extent, I've no idea), but mainly yes, higher FPS = more and more aggressive zombies.

Not sure what you mean by first zombie spawn, do you mean the prologue section where zombies first enter the mall?