During reassembly, once the two screws are in the left and right hinges, close the laptop and flip it over so that the display is down on the table. Run your fingers along the edge of the laptop where the display meets the lower assembly. If it is not flush, loosen the two screws in the hinges slightly and adjust, then retighten.
My macbook air's configuration (Mid-2011 core i5) has a different battery connector. It slides into a receptacle on the logic board. If your battery connector does not look like the one pictured, use the pointy end of a spudger to depress the small indentation in the middle of the battery connector cable terminal, and pull aft to release the clasp mechanism.