Your alarm is partially working correctly. Yes it is supposed to alarm without oil pressure BUT only if the engine RPM is above a certain threshold (i.e. its running, I believe the rpm cutoff is 300 but would have to look in the MEFI tables). If not the alarm should silence after about 2 seconds.

It's the way it's wired. Some features are only powered on when the key is on, like drives, tabs, gauges, and whatever else I'm not familiar with the boat yet so I can't say.

I would think you want to be able to access full accessories and mechanicals minus the engines running in case you had to work on something, and all of this without buzzers going crazy while you are doing it.