I would turn OFF File and FTP sharing. Those things slow down your computer and you don't need them to use LimeWire anyways.
I would also disable chat, since there is never any reason to send abusive messages to a host you are downloading from.
With regards to some of the other issues - I HIGHLY recommend updating to Jaguar (10.2.x) if at all possible. I can't imagine what AppleTalk would have to do with keeping the LimeWire connection going. I think the Jaguar update addressed the issue of lost network connections when the machine goes to sleep.
Have you looked at the settings in the Energy Saver System Preferences? I believe you can set your machine to never sleep, but use a separate monitor display to just make the monitor go blank. Don't run a screen saver since that chews up cycles also. But the eMac is a G4 and should be able to fly through it.
Hope this helps.
blue