Can I Connect a Second Monitor Like This?

I'm pretty sure that you won't be able to add a monitor through the monitor that you already have. If you want to add a secondary monitor to your computer, I recommend getting another graphics card so that you can have more than one connected at the same time.

No, you are going to need another graphics card because the ports on monitors are only for in, and the computer wouldn't know if you plugged another monitor in anyways.

If your computer has them, you can both the DVI & VGA outputs. As the others stated, daisy chaining monitor-to-monitor most likely will NOT work.

That definitely won't work because the DVI plug on your monitor is input, while your monitor will need to be plugged into an output source

No the plug on the bottom of your monitor is most likely INPUT and not OUTPUT. I would suggest, like the others, gettin a graphics card that supports multiple monitors.

That won't work, seeing as the port on your monitor is an input not an output. You'll need to get a splitter or a graphics card with more than one output.

The DVI most likely would be an input but even if you have an output one like me it's only a loop through so it would mirror your existing monitor

The question doesn't provide enough information. All of the computers at my college have a standard video-out and a DVI. They have splitters for the DVI, so you can plug two monitors into the one DVI slot, and the OS recognises this as an extra screen. I'd assume that plugging a monitor into your standard video output would also result in a screen that the OS recognises as an extra screen.