Yes, you can.
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 difference between an N and a G router is all in what the purpose of your router is for. You need to see if you are using it for a personal or business use.
Yes. It will operate as a G network.
Yes.
802.11
In the wireless properties choose "compatibility mode for G" or something like that. If you do so your router will allow both types of wireless cards G and N.
The Linksys Dual-band Wireless A+g Notebook/laptop Router is good.
The same as with wireless G card and G router.
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.
no course you cant you bellend
If your router is configured to work in G mode only, then the answer is yes. If the router is configured to use mixed mode (B and G), then the answer is no. N type adapters will perform as they are supposed too (if the router is configured properly).