1) With 1.67 GHz you can go up to OS 10.5. Make sure you have enough RAM to run the system you wish to install. At least double what Apple says for minimum.
Mac OS X 10.4 Tiger system requirements - http://docs.info.apple.com/article.html?artnum=301341
Leopard 10.5 Technical Requirements - http://support.apple.com/kb/SP517
Note some applicaiton will no longer work with Leopard, in particular anything requiring Classic.
List of Applications Not Compatible with Leopard - http://guides.macrumors.com/List:Applications_Not_Compatible_with_Leopard
Have fun trying to find discs, and be prepared to pay a lot.
Texas Mac Man, Leopard disc sources - https://discussions.apple.com/thread/3636662
"a brody" post about upgrading to Leopard - https://discussions.apple.com/thread/3373795
Your Mac has built-in Airport Extreme Card with 802.11g support. If you need more speed than 33 Mbps on your wireless connection, you'll want an 802.11n wireless ethernet bridge, connecting your G5 to the ethernet LAN port of the bridge. Not all are compatible with all Mac operating systems. Apple's Airport Extreme base stations tend to be more compatible. Note those that were made prior to 2007 may not support 802.11n. While you can upgrade to 10.5, you'll lose access to Mac OS 9 applications.