Usually they are, you have configure the router for G wireless networks.
A Wireless G router provides Wireless access to 802.11g compatible devices
Rather no than yes. It will work if the router is configured to work in the "G" mode.
Yes, you can. Wireless N devices are reversely compatible with G networks.
Yes it is backwards compatible
No they do not. They simply have to work on a compatible frequency. Such as wireless a, b, g etc.
You can get a wireless router repeater at amazon.com or from your local electronic store. The repeater you choose must be compatible with your router http://www.amazon.com/Belkin-F5D7132-Wireless-G-Universal-Extender/dp/B000FTLOL0
Yes, if you connect them using a LAN cable.
Yes, a wireless n adapter is backwards compatible with wireless g. Check the box you are buying and it will tell you if it is compatible with which wireless ranges.
Yes. Wireless N routers are backward-compatible with wireless G cards. You will not get the performance benefits of N though.
It depends on which wireless adapter you are using for your xbox. You should have G or N.
The same as with wireless G card and G router.
Most 802.11n routers are backward compatible and will support 802.11g.