I know that one can install command-line linux distros on android. I also know that the screen resolution can be changed. I have a laptop screen with vga input laying around that I was hoping to turn into a small netbook for school with my phone as a processor. However, I have the droid razr m and I can't find (online) any way to output video so I can use the laptop screen. So my question is: How do I output the phone screen to VGA/HDMI as cheaply as possible?
I don't think there is a way to do this with this phone. The Droid Razr M doesn't support MHL, and its Android version is too old to have the feature of mirroring the screen to a Chromecast. You could still use Chromecast to send specific video (i.e. from movie players, presentation apps, or YouTube) to anything that has HDMI input, but not to mirror the whole screen.
Note that the phone's screen itself doesn't use a high-level protocol like VGA or HDMI, so you can't simply take the screen off, cut its ribbon cable, and wire a VGA screen in its place.