Negative terminal of what? If you unsure don't anyhow remove things and start engine. Worst thing could happen is damaging the engine because you meddle without knowing what.

In original conditions, you should see your voltage going up more than 12V when the engine is idle. Turning on other electrical device would make the voltage drop. Driving your car would make the voltage goes up. These are normal electrical specifics.

Humming noise due to alternator are mechanical problem, you may still see normal voltages.
Go get a mechanic to check it up.

By removing the battery, you may damage the alternator and possible other electronic components; including your computer.

When your engine is running, your solenoid will draw high current from both alternator and battery, powering the spark plug. Since you disconnect the battery, the alternator voltage will drop when heavy current is drawn. To counter the voltage drop, the alternator will push up the output voltage. Sometimes it creates higher surge voltage that may fry the electronics.

The battery is there to prevent too much surge voltage happening. Your voltage meter will not able to record these spikes.
Does the humming sound change when you accelerate?