4. Can I make this work using just my notebook's LCD display?
The desktop video card outputs to it's HDMI/VGA/DVI connector. The notebook's LCD display uses a LVDS input on your systemboard with no external jack to connect to it. Meaning then they cannot be physically connected together unless adapt a US$30 ebay kits allowing external input to the internal LCD as discussed, which only quite an advanced user would ever attempt.
Another more elegant solution would use a HDMI input expresscard as described at Play PS3/X360 on laptop screen using new HDMI Input Express Card. . Though current costs of $170 for the item makes it unattractive AND you'd need to then do a mPCIe eGPU implementation.
There are however these less drastic ways of getting your accelerated graphics card to render to the internal LCD, all of which will have lower performance than when running using an external LCD:
NVIDIA Optimus driver provides a transparent internal LCD cloning mode for systems with a 4500MHD/HD/HD3000/HD4000 iGPU primary video when using a NVIDIA GTS4xx/GTX4xx card.
Use Lucidlogix virtu drivers to provide transparent output using the internal LCD if you have a Sandy Bridge cpu. (timohour)
Ultramon/Chung Gun method can clone from the desktop eGPU's window to the internal LCD for windowed games/apps.
USB 3.0 framegrabbers have sufficient bandwidth to capture the image from the desktop eGPU and pipe it back to your notebook's display.
It is not feasible to use USB 2.0 framegrabbers. The desktop video card outputs HDMI/S-Video. To try to clone the output from the desktop video card via a USB frame grabber can be done, but consider say 1280x800x32-bit = 4MB per image. If gaming at 30FPS that's 120MB/s bandwidth required. USB 2.0 is 480Mbps (60MB/s in *best case* scenario.. more like 30MB/s in real-life).
Source:
http://forum.notebookreview.com/e-gpu-external-graphics-discussion/418851-diy-egpu-experiences.html
Credits: nando4
Problems? See this thread at archive.org.