The top and bottom aren't displayed fully on an NTSC TV. The screen size is 240 pixels, but once the it's trimmed down to NTSC TV size it's more like 224 pixels (and even less on some TVs).
And yeah, for a player made of several sprites you'll need to move them all. I've been working on some sprite animation code recently, I've figured a good way to do it is to have the engine move one sprite (the 'main' one), then the animation code draws the rest of the player sprites relative to that one. It keeps things simpler, though the code might be somewhat slower.