Okay Andrew, I will try to answer your questions. I use Lazarus in WinXP and Linux environments and I can honestly say that there is very little difference between the two.
1. Fedora will do fine. As it uses the RPM package install system you should have no trouble getting Lazarus up and running. I use Mandriva 2006 and the install system is pretty much the same.
2. Don't know too much about networking, but, you are using the 'front end' of the components not the 'nuts and bolts'. How they work is a matter for the underlying code of Lazarus.
3. If you want Delphi compatibility use the Delphi switch, works well.
4. An application coded on any Linux distro will run on every distro. Again its the underlying mechanics that determine everything.
5. Yes, it compiles into a single executable apart from support files of course (images database files etc).
I find that the Windows version is not as stable as the Linux version, it seg faults regularly on my WinXP box.
Have fun,
Tim