A:Answer Yes you can do that, but it may be better if you move the NETGEAR to a more central location, or at least run an ethernet connection (long patch cord) to where you plan to have your Airport Extreme.
If the structure of your apartment interferes with the signal, and you can't run ethernet to your bedroom, then consider something like a Power-to-Ethernet Bridge:
http://www.bestbuy.com/site/networking-accessories/powerline/pcmcat161100050043.c?id=pcmcat161100050043