Can you play a Nintendo Gamecube on a PC monitor?

I have a laptop and got an HDMI adapter for my Nintendo Gamecube to play on my laptop, only to find out that my laptop doesn't have the right HDMI port (one output, not one input).

Does a separate PC monitor have a suitable HDMI connection, and could I then use it as a screen, as should normally be the case with a TV?

Do I have to connect the PC monitor to my laptop first, and can I do that at all? Can a PC monitor work alone, only connected to the Gamecube console?

Any display device with a graphic input can do that.
A monitor or television makes no difference!

Your laptop has only one outlet, but you know that now

How do I know that a monitor has a graphics input? Can or do I have to connect it to my laptop in advance to be able to play with the console?

A monitor is designed to receive and display an image from an external system.
A monitor always has a graphic input!