Neither the WRT54G, nor the WAP54G can act as repeaters. They require a wired connection. I do not know of anyone at the SOHO class level who is offering a 802.11g repeater. Cisco does offer one, but it is $3,500.
If your primary need is internet access, and LAN transfers are relatively less an issue, you could do either:
1. Powerline ethernet bridges between router #1 and router #2. I have used the Sieman's powerline adapters in exactly this fashion. They operate at 14 mbs, which is likely substantially faster than your internet connection. They are low latency. I just bought two for $79.99 after rebates from CompUsa.
2. You could use an 802.11b wireless ethernet bridge, or an 802.11g wireless ethernet bridge. Linksys is the only manufacturer I know of for these items. The briddge device would provide the wireless-to-wired connection you need between router #1 and router #2. A WET11 will run about $90; the WET54G (if you can find one) about $180.
Since you can move the location of the second wireless router around with some freedom, why not see if you cannot run a piece of CAT 5 cable to tie the two routers together? If the house has central air or heating, you can run through the ducts. Total cost would be less than $10 in parts.
Q2: Why do they need different channels? So they do not interfere with each other. Traditionally access points are spread out in a channel 1-6-11 sequence.
