The eMac cannot be used as a second monitor. However you might be able to use a second monitor with the eMac. For iMacs and iBooks, there is ScreenSpanning Doctor, but I'm not sure whether it works with eMacs as well. Just google for it and give it a shot. I used it with all iBooks I have owned and it worked great!
Also, OS X likes RAM, so upgrading to 1 GB will probably improve performance.
Upgrading the OS does not speed up things by orders of magnitude, i. e. noticeably.
iPhoto 2 (I don't think there ever was a version 3) was slow as a dog, so upgrading iLife will be an improvement.
To be honest, if I were in your place, I would worry about the monitor. I worked with some eMacs and once you are used to lcd screens, you never want to go back
