The part you said was missing from your car is OK to go without. This is common especially if you have an SRI
. The top is usually just snapped in to the front of the box, and the bottom is left hanging, open and unattached to anything.
Its basically a duct that allows air flow through the electrical parts inside the electrical component box.
Also, it is normal for your car to idle lower than 1k when the car is hot or the air in/around your engine is hot (summer temps). And conversely, it's also normal for your engine to idle a bit over 1k when it's cold or the air is cold (winter temps).