Yes, the impeller goes in that housing. It is the raw water pump.
The bilge water may be oily because some oil was spilled during an oil change. For example, it is easy to spill oil removing the filter. There is no way to know whether it is caused by accident or if you have a small oil leak. I would go out and buy some sort of bilge cleaner, I got mine on sale from Overton's for $1.99. Give the bilge a good cleaning and see if the oil comes back. Alternatively, you could monitor the oil level of the engine, v-drive unit, and transmission to make sure none are leaking. However, you'll want to clean the bilge out anyway, unless you enjoy dumping polluted water into the places you boat and swim.
1996 Prostar 190, 350 TBI and Powerslot