I have about 10 web-sites, and I only registered one on Amazon associates program. Can I use my special links on the rest of my web-sites? or is this illegal?
Yes, you can use your affiliate links on as many sites you own. Just don't break Amazon's Operating Agreement.
While you can use the same links on as many sites as you would like it's probably best to create a new tracking ID for each of your sites so that you can filter down reports for each site and see a clearer picture of how each site is performing. This will also help you to prove income levels if you decide to sell your sites in the future.