No.
a lot faster
Rather no than yes. It will work if the router is configured to work in the "G" mode.
A Wireless G router provides Wireless access to 802.11g compatible devices
Your wireless adapter probably worked better with the old router. Or the new router is a lower end N router and the old one was a high end G
The same as with wireless G card and G router.
Usually they are, you have configure the router for G wireless networks.
PS3 has a G signal, but when you purchase your wireless router you are better off getting the Wireless-N-Broadband router for future connections to other devices. PS3 also is better wired than wireless and I found the signal test of the PS3 much better wired than WiFi. I also brought my Linksys by Cisco model no WRT160N wireless router at Best Buy and later saw a much better model at Sam's Club for the same price range that Best Buy had for twice the price
You can use router of G or N type and the same type wireless adapter. Of course you can use wireless N adapter with G-type router and reverse.
Yes, however, your internet speed will only be that of the G router which is comparably slower than that of an N router.
The BELKIN Wireless G Router 5X FASTER has a 400ft RANGE.
Wireless N routers have better range and much better transfer speeds than G routers.
There are many places where one can buy a Belkin G wireless router. One can purchase a Belkin G wireless router at popular mass retail stores such as Walmart, Target, or Best Buy.