I use a home-built router and a TP-link WiFi access point, works great! Building your own router is as simple as having a Linux box with two ethernet plugs and installing a DHCP server, and some iptables tweaking for NAT.
That depends. There has been low-power CPUs along the history, if you manage to find a box with one of those then I wouldn't be surprised if you get way below 50W. Of course that probably is still significantly more than what an embedded solution would consume, but on the other hand you should get better performance and more flexibility. You could use the same box for eg NAS.
 Intel ARK finds 108 =<35W desktop CPUs, from the original Pentiums to modern day i5 Ivy Bridges.
Linux runs on Linksys routers (dd-wrt, for example), so Linux != lots of power :) There are some cool boards you can get pretty cheap with 10/100 ethernet, which is probably all you need for an internet conneciton (I have 60 up/down at home so it's enough for me).