Yes
If you just connect a router to your iPhone, then the Internet should be free.
Yes, any phone that supports WiFi (also reffered to as 802.11g) is able to go on the internet through your router if you are close enough to it (i.e. in your house). An example is Apple's iPhone.
External access through the Internet.
no, you just have to have a wi-fi router and Internet
# You could try using your router.
no
The iPhone 3G should connect to just about any wireless internet router or provider, provided you have the password. Passwords vary depending on what kind of router is being used but all can be obtained.
A router is useful to establish a wireless connection to the internet through a wireless device. A router in some cases is the only way to establish a connection, and is much simpler than wiring your device to the modem itself for a connection.
It could be your router. Try resetting the router, since there is usually a small reset button on a router somewhere. If it is not your router, try looking through your Wi-Fi settings. You may have restricted internet access.
Yes, the standard is backwards compatible.
A wired or wireless router.
No Internet on the iPod Touch is free! But, you must have a wireless router (Wi-Fi) for the iPod to connect to the Internet through your router's Internet.