No.
a lot faster
Rather no than yes. It will work if the router is configured to work in the "G" mode.
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
A Wireless G router provides Wireless access to 802.11g compatible devices
The same as with wireless G card and G router.
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
Usually they are, you have configure the router for G wireless networks.
Yes, however, your internet speed will only be that of the G router which is comparably slower than that of an N router.
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.
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.