Please take a minute and check out this blog post
to learn a bit more about the new search feature and its options. In Gamepedia Mobygames is a very good search site. Make sure it's turned on in your Preferences/Sites and either move it to the top of your list or select it from the magnifying glass in the search window for targeted searches on that site only. For DVDpedia, IMDb is a great resource or TV Rage and the TVDb for TV series. For Bookpedia, check out Wikipedia, Freebase and OpenLibrary.
The reason the associate ID sign up asks you for website info is because the associate ID is used for link backs and ultimately commissions. Amazon requires that all queries on their web services (AWS) are 'signed' by an associate ID so that if any sales happen on visits to Amazon using that ID, the commission can be paid back.
This means for example that if you upload your Gamepedia collection to the web and someone clicks on a link there to Amazon and ends up buying something you will receive a commission for that purchase from Amazon. The same is true for links to Amazon clicked on directly through the program.
The reason we've moved the Amazon searches to be a sign up option rather than an incorporated one is because we've had several issues with their services in the past, most importantly regarding our iPhone app which we had to remove from the App Store twice because of complaints from Amazon. With this new system, those issues will hopefully be taken care of for good. We'd also rather pass the commissions on to our users.(To sign up for the associate ID you can use anything, even a Twitter feed.)