Orientation doesn't matter but the pattern of batteries does. The batteries should be alternating as shown here.

The battery cage is a bit loose but it doesn't matter. It will work.

To close the lid, slide it in from the bottom as pictured below. It will be very snug. You may want to press the batteries down with your fingers to ease the lid on.

If you cut the length and bend the wires correctly, they should stay in the slots by themselves and be wedged tighter upon closing the lid. You can always use a bit of glue to hold them down but be careful not to have them sticking out too much or else the lid won't close.