Interestingly you can get out DPI display signal from GPIO pins. Adafruit is using this technique with their Kippah display, giving you fully accelerated display signal (unlike those crappy low-fps-low-res framebuffer driven GPIO displays).
Correct. My understanding is that trick was made possible by design -- one of their engineers specifically chose pins to bring out to the GPIO header to facilitate it.
I've seen some variants on the "Kippah" to directly drive VGA.
No. The Raspberry Pi GPIO header doesn't include all pins, and in particular it doesn't include pins that were used for other peripherals, such as the camera and display interfaces.