Installing a router

I believe he means a wireless bridge, which is a router that connects to another router and connects the wired clients to the wireless network. I use a second wireless router as a bridge to connect my PC and other things to the wireless without having several wireless cards. Standalone bridges are sold (usually overpriced) or you can flash many routers with OpenWRT, DD-WRT, etc. and get bridging functionality without paying a premium.

Mind you, if you also have a PC or laptop in the same room that's using the wireless, you can accomplish the same by using Internet Connection Sharing.

I had something like this in mind.

No. Not at all. First off, the signal is only so strong that it won't travel very far. It's usually only limited to in-house. You have a greater chance of sharing internet with the neighborhood using a wireless signal than with powerline networking.

Second, each powerline adapter is encrypted so they will only talk to each other. Any new adapter you add outside of what you get in the kit has to be configured to talk to the other adapters (using the software provided by the manufacturer). So, anyone not using the same key (128-bit AES) can't connect to your network.