The black plastic cover to which you refer goes on the deck - it's a pulley cover. The auto blade stop are the steel 'pedals' attached to the deck.
The plastic is just a safety cover. If you're keeping it, and don't care, it isn't really needed. The screws tend to fall out of the cover, or they had a lot of belt problems, and it usually found its way into the garbage.It makes the whole thing look a little cleaner, though.
That style seat (but with the Snapper logo on it) isn't available anymore, but any plain jane lowback replacement seat will work.
That blade has the 'hi-vac' wings on it, they are used for more lift/blow with a bagger unit. If you're not going to use a bagger - I'd take them off and sharpen the blade. Looks like you have one sharpening left, IMHO.
BTW, I'm sure you know that steering 'wheel' is on 180 degrees upside-down. The white ones didn't have that style wheel, they used a metal yoke.
She's a tad rough, but keep us posted! I've messed with worse!