Is it allowed under the rules and ask the Affiliate Program website containing a part of their name? For example: amazontv.com
You're not allowed to do anything that might lead people to believe that you're associated with Amazon in any capacity other than as an associate. If you put a prominent disclaimer you probably could get away with it but you're probably better off finding another domain.
No - you can't include 'Amazon' in the domain name. It violates Amazon Associates Operating Agreement (Section 2 [f])
Actually, you can't use any trademark in the domain name, if you're going to use Amazon, as there's a very high chance they will terminate block your website. Personal experience, it happened to me.
Try to be sure about the trademark of domain name before using any. More specifically, it's better not to try with some giant's name or something that may seem as their affiliate. It may cause even legal problem for you.
You cannot use amazon name in anyway in domain name. be quick and get the site down. If Amazon finds your site, ur account will be permanently terminated.