Does the gauge indicate an oil pressure drop if the engine oil level goes down? And, does the sensor for this gauge also go into the oilpan?

 

By the time you see a drop in oil pressure due to low oil level, it may be too late for your engine because this means that the level is so low the pump is beginning to suck air along with the oil.
You don't use a pressure gauge to check level, you do that by looking at the dipstick regularly. If you do see a drop in pressure that is not normal (the pressure WILL normally drop as the engine warms up and reaches its operating temperature, you'll learn what the normal hot pressure is after a while), the cause must be found as soon as possible to prevent engine damage. It could just be time for an oil change, or there could be a problem with internal engine components.
The sensor does not go in the pan, it can't read pressure there. A sensor for oil TEMP can go in the pan, usually in the drain plug. The pressure sensor goes in an oil galley on top of the engine.