Shoutbox

1. Yes

2. Yes

3. No.  802.11 b/g is what it is, regardless what else one end might support. If you gain any additional range, it would be coincidental and due to the design differences of the new router (all consumer grade products operate at some small fraction of the permitted maximum power and have less-than-optimal antennas; obviously, some suck less than others).

4. Usually not for people who just want wireless Internet access, unless they have ungodly fast Internet or truly need the range (in which case they must get 802.11n hardware on both ends).  If you are doing home networking between your computers, working with large files, etc.  then yes, it could benefit you. 

SonicSam's point doesn't stand because the stated transfer rates of all 802.11 protocols are best case, which almost never is your case.  In reality, depending on the distance, terrain and interference level, all the protocols will be falling back quite a few notches to maintain reliable communications.  Unless you are sitting right next to your access point, you may need 802.11n just to get the 54Mbps you might presently be expecting from 802.11g.  I've seen marginal WiFi connections fall back to dialup modem speeds of the 90s.