1) Networking isnt CPU specific, and is designed to be cross platform, so yes you can network a AMD system to a Intel one.
2) Gigabit isnt required for 3d gaming, you will probably find that 100mb is fine for gaming, think of it this way when you play on line you play on a smaller connection the 100mb.
3)It doesnt really slow a system down playing on a LAN
4)The LAN socket will be using power from your motherboard regardless of whether or not its being used.
5)There is nothing stopping you playing games on Windows 98 against someone on Windows XP
Hope this helps