Yes. It will not have the same performance as a N receiver, but they will connect and work.
It will not benefit from its increased throughput capability but it will benefit from the signal enhancement as it is the transmittor so lnog as the receiver is in range.
Wireless routers are required to have a wireless network connection. The stronger the wireless signal the further the signal will reach. Although the network can be seen by others within it's signal range, for security reasons your network cannot be accessed without a network key. Specifically a N rated wireless router has a powerful signal. G routers are much less powerful. For any router to work you need to connect a wireless receiver to the computer you want on the network.
You can purchase so called wireless range extender, it does exactly what you need.
A Wireless G router provides Wireless access to 802.11g compatible devices
A Wireless N router simply uses different types of Hardware, the exact piece is called a N Connector. This allows for the router to not only put out a wireless signal, but it also allows for the router to receive wireless signal. This works great for computers that cannot pick up wireless signals normally.
The same as with wireless G card and G router.
Could be interference. Wireless G routers use 2.4 Ghz, some wireless phones also use that frequency. Could be interference with another router, too. Could be weak signal, or if there's metal in close proximity, especially a chain link fence.
No.
Usually they are, you have configure the router for G wireless networks.
If you are currently using G then step up to N and also make sure to buy a wireless N receiver for your computer or the router is useless. If you are currently using G then step up to N and also make sure to buy a wireless N receiver for your computer or the router is useless.
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.
There is no guarantee, but if you are lucky... Make sure that your router works in the compatibility mode (G+N). Of course the extender will be able to transmit G network signal.