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.
one is better
Speed and technology (N is a newer, faster technology.)
They are two different protocols. Most (probably all) N routers and networks cards can also do G and probably B protocol. Anything labeled as G will only do G and in amlost all cases B. N is faster than G (but you'd never notice the speed difference if you are just connecting to the internet, they are both way faster than a home internet connection. N should, technically, have a bit longer range than G, but in real-life most people don't see a great deal of difference here.
The same as with wireless G card and G router.
Yes, however, your internet speed will only be that of the G router which is comparably slower than that of an N router.
No.
You can't and you don't want to. A "N" router will work with "G" network components and will additionally support "N" hardware at a higher speed. Converting it to "G" would be a step down.
The equipment with the "n" designation can transmit data at twice the speed of "g" routers and is more than five times as fast as "b" wireless routers.
N is better. It is faster.
Usually they are, you have configure the router for G wireless networks.
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.
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.