ML 320, Stuff Running?

Well...My wife has traded her SDL for an 1998 ML 320. Now I get to figure it out and need some help.
When the engine is shut-off, there is a cooling fan in the electrical box that continues to run for several minutes, the aux. water pump also runs for the same time. Is this normal? Is something overheating? What is the issue and is it something I need to persue?

Also, basing this on the excellent guidance my other requests received, the "master Lock" system on this truck works from the console button, but not with the drivers door key or the remote.
Any paericular place to start running this problem down.

Many thanks in advance.